MinT - Information on Result #1198068

Information on Result #1198068

Digital (84, 101, 1048764)-net over F₂₇, using net defined by OOA based on linear OOA(27¹⁰¹, 1048764, F₂₇, 18, 17) (dual of [(1048764, 18), 18877651, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(27¹⁰¹, 4195057, F₂₇, 2, 17) (dual of [(4195057, 2), 8390013, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(27²⁰, 756, F₂₇, 2, 8) (dual of [(756, 2), 1492, 9]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(27⁰, s, F₂₇, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      3. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      4. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      5. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      6. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      7. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      8. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      9. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      10. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      11. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      12. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      13. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      14. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      15. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      16. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      17. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      18. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      19. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      20. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(27¹, s, F₂₇, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      21. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
      22. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
      23. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
      24. linear OOA(27², 28, F₂₇, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;54,27) [i]
      25. linear OOA(27², 28, F₂₇, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code) (see above)
      26. linear OOA(27⁴, 28, F₂₇, 2, 4) (dual of [(28, 2), 52, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;52,27) [i]
      27. linear OOA(27⁸, 28, F₂₇, 2, 8) (dual of [(28, 2), 48, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;48,27) [i]
  2. linear OOA(27⁸¹, 4194301, F₂₇, 2, 17) (dual of [(4194301, 2), 8388521, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(27⁸¹, 8388602, F₂₇, 17) (dual of [8388602, 8388521, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁸¹, large, F₂₇, 17) (dual of [large, large−81, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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.