Best Known (38−18, 38, s)-Nets in Base 27
(38−18, 38, 146)-Net over F27 — Constructive and digital
Digital (20, 38, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (7, 25, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 13, 64)-net over F27, using
(38−18, 38, 182)-Net in Base 27 — Constructive
(20, 38, 182)-net in base 27, using
- (u, u+v)-construction [i] based on
- (3, 12, 82)-net in base 27, using
- base change [i] based on digital (0, 9, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- base change [i] based on digital (0, 9, 82)-net over F81, using
- (8, 26, 100)-net in base 27, using
- 2 times m-reduction [i] based on (8, 28, 100)-net in base 27, using
- base change [i] based on digital (1, 21, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 21, 100)-net over F81, using
- 2 times m-reduction [i] based on (8, 28, 100)-net in base 27, using
- (3, 12, 82)-net in base 27, using
(38−18, 38, 527)-Net over F27 — Digital
Digital (20, 38, 527)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2738, 527, F27, 18) (dual of [527, 489, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2738, 740, F27, 18) (dual of [740, 702, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(2735, 729, F27, 18) (dual of [729, 694, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2727, 729, F27, 14) (dual of [729, 702, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(273, 11, F27, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,27) or 11-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2738, 740, F27, 18) (dual of [740, 702, 19]-code), using
(38−18, 38, 176320)-Net in Base 27 — Upper bound on s
There is no (20, 38, 176321)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2 465073 109657 109677 961628 110706 541320 817040 488200 183611 > 2738 [i]