Best Known (73, 110, s)-Nets in Base 27
(73, 110, 1094)-Net over F27 — Constructive and digital
Digital (73, 110, 1094)-net over F27, using
- 272 times duplication [i] based on digital (71, 108, 1094)-net over F27, using
- net defined by OOA [i] based on linear OOA(27108, 1094, F27, 37, 37) (dual of [(1094, 37), 40370, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(27108, 19693, F27, 37) (dual of [19693, 19585, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(27108, 19694, F27, 37) (dual of [19694, 19586, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(33) [i] based on
- linear OA(27106, 19683, F27, 37) (dual of [19683, 19577, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2797, 19683, F27, 34) (dual of [19683, 19586, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(272, 11, F27, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- construction X applied to Ce(36) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(27108, 19694, F27, 37) (dual of [19694, 19586, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(27108, 19693, F27, 37) (dual of [19693, 19585, 38]-code), using
- net defined by OOA [i] based on linear OOA(27108, 1094, F27, 37, 37) (dual of [(1094, 37), 40370, 38]-NRT-code), using
(73, 110, 15327)-Net over F27 — Digital
Digital (73, 110, 15327)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(27110, 15327, F27, 37) (dual of [15327, 15217, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(27110, 19691, F27, 37) (dual of [19691, 19581, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,17]) [i] based on
- linear OA(27109, 19684, F27, 37) (dual of [19684, 19575, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(27103, 19684, F27, 35) (dual of [19684, 19581, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,18]) ⊂ C([0,17]) [i] based on
- discarding factors / shortening the dual code based on linear OA(27110, 19691, F27, 37) (dual of [19691, 19581, 38]-code), using
(73, 110, large)-Net in Base 27 — Upper bound on s
There is no (73, 110, large)-net in base 27, because
- 35 times m-reduction [i] would yield (73, 75, large)-net in base 27, but