Best Known (59, 59+14, s)-Nets in Base 27
(59, 59+14, 1198399)-Net over F27 — Constructive and digital
Digital (59, 73, 1198399)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (52, 66, 1198371)-net over F27, using
- net defined by OOA [i] based on linear OOA(2766, 1198371, F27, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2766, 8388597, F27, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2766, large, F27, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2766, large, F27, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2766, 8388597, F27, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(2766, 1198371, F27, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- digital (0, 7, 28)-net over F27, using
(59, 59+14, large)-Net over F27 — Digital
Digital (59, 73, large)-net over F27, using
- 272 times duplication [i] based on digital (57, 71, large)-net over F27, using
- t-expansion [i] based on digital (56, 71, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2771, large, F27, 15) (dual of [large, large−71, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2771, large, F27, 15) (dual of [large, large−71, 16]-code), using
- t-expansion [i] based on digital (56, 71, large)-net over F27, using
(59, 59+14, large)-Net in Base 27 — Upper bound on s
There is no (59, 73, large)-net in base 27, because
- 12 times m-reduction [i] would yield (59, 61, large)-net in base 27, but