Best Known (36−14, 36, s)-Nets in Base 27
(36−14, 36, 252)-Net over F27 — Constructive and digital
Digital (22, 36, 252)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 28)-net over F27, using
- s-reduction based on digital (0, 1, s)-net over F27 with arbitrarily large s, using
- digital (0, 1, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27, using
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 3, 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 (0, 4, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 7, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 14, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 1, 28)-net over F27, using
(36−14, 36, 937)-Net in Base 27 — Constructive
(22, 36, 937)-net in base 27, using
- base change [i] based on digital (13, 27, 937)-net over F81, using
- net defined by OOA [i] based on linear OOA(8127, 937, F81, 14, 14) (dual of [(937, 14), 13091, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8127, 6559, F81, 14) (dual of [6559, 6532, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(8127, 6559, F81, 14) (dual of [6559, 6532, 15]-code), using
- net defined by OOA [i] based on linear OOA(8127, 937, F81, 14, 14) (dual of [(937, 14), 13091, 15]-NRT-code), using
(36−14, 36, 2012)-Net over F27 — Digital
Digital (22, 36, 2012)-net over F27, using
(36−14, 36, 2150)-Net in Base 27
(22, 36, 2150)-net in base 27, using
- base change [i] based on digital (13, 27, 2150)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8127, 2150, F81, 3, 14) (dual of [(2150, 3), 6423, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8127, 2187, F81, 3, 14) (dual of [(2187, 3), 6534, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- OOA 3-folding [i] based on linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(8127, 2187, F81, 3, 14) (dual of [(2187, 3), 6534, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8127, 2150, F81, 3, 14) (dual of [(2150, 3), 6423, 15]-NRT-code), using
(36−14, 36, 2987061)-Net in Base 27 — Upper bound on s
There is no (22, 36, 2987062)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3381 394839 550405 297097 676899 467609 316590 091944 131177 > 2736 [i]