MinT - Information on Result #1197344

Information on Result #1197344

Digital (13, 21, 382)-net over F₂₇, using net defined by OOA based on linear OOA(27²¹, 382, F₂₇, 10, 8) (dual of [(382, 10), 3799, 9]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(27²¹, 765, F₂₇, 2, 8) (dual of [(765, 2), 1509, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(27²¹, 766, F₂₇, 2, 8) (dual of [(766, 2), 1511, 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(27⁹, 38, F₂₇, 2, 8) (dual of [(38, 2), 67, 9]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,67P) [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
        a function field by SÃ©mirat [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

The following results depend on this result:

	Result		This result only	Method
1	Digital (81, 97, 1048957)-net over F₂₇	[i]		(u,Â u+v)-Construction for Nets
2	Digital (85, 102, 1048957)-net over F₂₇	[i]		(u,Â u+v)-Construction for Nets