Best Known (40, 40+23, s)-Nets in Base 27
(40, 40+23, 290)-Net over F27 — Constructive and digital
Digital (40, 63, 290)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- 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, 3, 28)-net over F27 (see above)
- digital (0, 4, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 5, 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, 11, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (1, 24, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
(40, 40+23, 597)-Net in Base 27 — Constructive
(40, 63, 597)-net in base 27, using
- net defined by OOA [i] based on OOA(2763, 597, S27, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(2763, 6568, S27, 23), using
- discarding factors based on OA(2763, 6569, S27, 23), using
- discarding parts of the base [i] based on linear OA(8147, 6569, F81, 23) (dual of [6569, 6522, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(8145, 6561, F81, 23) (dual of [6561, 6516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(8147, 6569, F81, 23) (dual of [6569, 6522, 24]-code), using
- discarding factors based on OA(2763, 6569, S27, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(2763, 6568, S27, 23), using
(40, 40+23, 4384)-Net over F27 — Digital
Digital (40, 63, 4384)-net over F27, using
(40, 40+23, large)-Net in Base 27 — Upper bound on s
There is no (40, 63, large)-net in base 27, because
- 21 times m-reduction [i] would yield (40, 42, large)-net in base 27, but