MinT - Information on Result #1227623

Information on Result #1227623

Digital (63, 74, 4431444)-net over F₈₁, using (u,Â u+v)-construction based on

digital (12, 17, 4194301)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81¹⁷, 4194301, F₈₁, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(81¹⁷, 4194301, F₈₁, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(81¹⁷, large, F₈₁, 5) (dual of [large, large−17, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
digital (46, 57, 2215722)-net over F₈₁, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 16, 538002)-net over F₈₁, using
    - net defined by OOA [i] based on linear OOA(81¹⁶, 538002, F₈₁, 5, 5) (dual of [(538002, 5), 2689994, 6]-NRT-code), using
      - appending kth column [i] based on linear OOA(81¹⁶, 538002, F₈₁, 4, 5) (dual of [(538002, 4), 2151992, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 4, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81⁰, 6642, F₈₁, 4, 0) (dual of [(6642, 4), 26568, 1]-NRT-code) (see above)
        linear OOA(81¹, 6642, F₈₁, 4, 1) (dual of [(6642, 4), 26567, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 4, 1) for arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OOA(81¹, 6642, F₈₁, 4, 1) (dual of [(6642, 4), 26567, 2]-NRT-code) (see above)
        linear OOA(81¹, 6642, F₈₁, 4, 1) (dual of [(6642, 4), 26567, 2]-NRT-code) (see above)
        linear OOA(81³, 6642, F₈₁, 4, 2) (dual of [(6642, 4), 26565, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81³, 6643, F₈₁, 4, 2) (dual of [(6643, 4), 26569, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(81³, 6643, F₈₁, 2, 2) (dual of [(6643, 2), 13283, 3]-NRT-code), using
        appending kth column [i] based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
        Hamming code H(3,81) [i]
        linear OOA(81¹⁰, 6642, F₈₁, 4, 5) (dual of [(6642, 4), 26558, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 4, 0) for arbitrarily large s (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81⁰, 82, F₈₁, 4, 0) (dual of [(82, 4), 328, 1]-NRT-code) (see above)
        linear OOA(81¹, 82, F₈₁, 4, 1) (dual of [(82, 4), 327, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 4, 1) for arbitrarily large s (see above)
        linear OOA(81¹, 82, F₈₁, 4, 1) (dual of [(82, 4), 327, 2]-NRT-code) (see above)
        linear OOA(81¹, 82, F₈₁, 4, 1) (dual of [(82, 4), 327, 2]-NRT-code) (see above)
        linear OOA(81², 82, F₈₁, 4, 2) (dual of [(82, 4), 326, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;326,81) [i]
        linear OOA(81⁵, 82, F₈₁, 4, 5) (dual of [(82, 4), 323, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;323,81) [i]
  2. digital (30, 41, 1677720)-net over F₈₁, using
    - net defined by OOA [i] based on linear OOA(81⁴¹, 1677720, F₈₁, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
      - OOA 5-folding and stacking with additional row [i] based on linear OA(81⁴¹, 8388601, F₈₁, 11) (dual of [8388601, 8388560, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.