Best Known (24, 24+22, s)-Nets in Base 27
(24, 24+22, 158)-Net over F27 — Constructive and digital
Digital (24, 46, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 29, 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 (6, 17, 76)-net over F27, using
(24, 24+22, 182)-Net in Base 27 — Constructive
(24, 46, 182)-net in base 27, using
- (u, u+v)-construction [i] based on
- (4, 15, 82)-net in base 27, using
- 1 times m-reduction [i] based on (4, 16, 82)-net in base 27, using
- base change [i] based on digital (0, 12, 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, 12, 82)-net over F81, using
- 1 times m-reduction [i] based on (4, 16, 82)-net in base 27, using
- (9, 31, 100)-net in base 27, using
- 1 times m-reduction [i] based on (9, 32, 100)-net in base 27, using
- base change [i] based on digital (1, 24, 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, 24, 100)-net over F81, using
- 1 times m-reduction [i] based on (9, 32, 100)-net in base 27, using
- (4, 15, 82)-net in base 27, using
(24, 24+22, 522)-Net over F27 — Digital
Digital (24, 46, 522)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2746, 522, F27, 22) (dual of [522, 476, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2746, 740, F27, 22) (dual of [740, 694, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(2743, 729, F27, 22) (dual of [729, 686, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(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(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(2746, 740, F27, 22) (dual of [740, 694, 23]-code), using
(24, 24+22, 182696)-Net in Base 27 — Upper bound on s
There is no (24, 46, 182697)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 696207 163685 922857 126663 473189 725389 289310 027324 209759 551904 916643 > 2746 [i]