Best Known (24, 47, s)-Nets in Base 27
(24, 47, 158)-Net over F27 — Constructive and digital
Digital (24, 47, 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, 30, 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, 47, 182)-Net in Base 27 — Constructive
(24, 47, 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, 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
- (4, 15, 82)-net in base 27, using
(24, 47, 446)-Net over F27 — Digital
Digital (24, 47, 446)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2747, 446, F27, 23) (dual of [446, 399, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2747, 737, F27, 23) (dual of [737, 690, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(2745, 729, F27, 23) (dual of [729, 684, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2739, 729, F27, 20) (dual of [729, 690, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(272, 8, F27, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2747, 737, F27, 23) (dual of [737, 690, 24]-code), using
(24, 47, 182696)-Net in Base 27 — Upper bound on s
There is no (24, 47, 182697)-net in base 27, because
- 1 times m-reduction [i] would yield (24, 46, 182697)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 696207 163685 922857 126663 473189 725389 289310 027324 209759 551904 916643 > 2746 [i]