Best Known (71, 93, s)-Nets in Base 7
(71, 93, 1528)-Net over F7 — Constructive and digital
Digital (71, 93, 1528)-net over F7, using
- 71 times duplication [i] based on digital (70, 92, 1528)-net over F7, using
- net defined by OOA [i] based on linear OOA(792, 1528, F7, 22, 22) (dual of [(1528, 22), 33524, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(792, 16808, F7, 22) (dual of [16808, 16716, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(792, 16813, F7, 22) (dual of [16813, 16721, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(786, 16807, F7, 20) (dual of [16807, 16721, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(71, 6, F7, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(792, 16813, F7, 22) (dual of [16813, 16721, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(792, 16808, F7, 22) (dual of [16808, 16716, 23]-code), using
- net defined by OOA [i] based on linear OOA(792, 1528, F7, 22, 22) (dual of [(1528, 22), 33524, 23]-NRT-code), using
(71, 93, 10669)-Net over F7 — Digital
Digital (71, 93, 10669)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(793, 10669, F7, 22) (dual of [10669, 10576, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(793, 16815, F7, 22) (dual of [16815, 16722, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(781, 16807, F7, 19) (dual of [16807, 16726, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [i]
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(793, 16815, F7, 22) (dual of [16815, 16722, 23]-code), using
(71, 93, large)-Net in Base 7 — Upper bound on s
There is no (71, 93, large)-net in base 7, because
- 20 times m-reduction [i] would yield (71, 73, large)-net in base 7, but