Best Known (30, 30+17, s)-Nets in Base 27
(30, 30+17, 336)-Net over F27 — Constructive and digital
Digital (30, 47, 336)-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, 1, 28)-net over F27 (see above)
- 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, 5, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 8, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 17, 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
(30, 30+17, 821)-Net in Base 27 — Constructive
(30, 47, 821)-net in base 27, using
- net defined by OOA [i] based on OOA(2747, 821, S27, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(2747, 6569, S27, 17), using
- discarding parts of the base [i] based on linear OA(8135, 6569, F81, 17) (dual of [6569, 6534, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(8133, 6561, F81, 17) (dual of [6561, 6528, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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]
- 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(16) ⊂ Ce(13) [i] based on
- discarding parts of the base [i] based on linear OA(8135, 6569, F81, 17) (dual of [6569, 6534, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on OA(2747, 6569, S27, 17), using
(30, 30+17, 4198)-Net over F27 — Digital
Digital (30, 47, 4198)-net over F27, using
(30, 30+17, large)-Net in Base 27 — Upper bound on s
There is no (30, 47, large)-net in base 27, because
- 15 times m-reduction [i] would yield (30, 32, large)-net in base 27, but