MinT - Information on Result #1224872

Information on Result #1224872

Digital (88, 101, 2797254)-net over F₃₂, using (u,Â u+v)-construction based on

digital (20, 26, 2796201)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32²⁶, 2796201, F₃₂, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
  - OA 3-folding and stacking [i] based on linear OA(32²⁶, large, F₃₂, 6) (dual of [large, large−26, 7]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
digital (62, 75, 1398627)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (8, 14, 527)-net over F₃₂, using
    - net defined by OOA [i] based on linear OOA(32¹⁴, 527, F₃₂, 10, 6) (dual of [(527, 10), 5256, 7]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OOA(32¹⁴, 1055, F₃₂, 2, 6) (dual of [(1055, 2), 2096, 7]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32¹⁴, 1056, F₃₂, 2, 6) (dual of [(1056, 2), 2098, 7]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32⁰, s, F₃₂, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32¹, s, F₃₂, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
        linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
        linear OOA(32², 33, F₃₂, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;64,32) [i]
        linear OOA(32³, 33, F₃₂, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;63,32) [i]
        linear OOA(32⁶, 33, F₃₂, 2, 6) (dual of [(33, 2), 60, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;60,32) [i]
  2. digital (48, 61, 1398100)-net over F₃₂, using
    - net defined by OOA [i] based on linear OOA(32⁶¹, 1398100, F₃₂, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
      - OOA 6-folding and stacking with additional row [i] based on linear OA(32⁶¹, 8388601, F₃₂, 13) (dual of [8388601, 8388540, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁶¹, large, F₃₂, 13) (dual of [large, large−61, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.