Best Known (25, 49, s)-Nets in Base 27
(25, 49, 158)-Net over F27 — Constructive and digital
Digital (25, 49, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 18, 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, 31, 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, 18, 76)-net over F27, using
(25, 49, 172)-Net in Base 27 — Constructive
(25, 49, 172)-net in base 27, using
- 23 times m-reduction [i] based on (25, 72, 172)-net in base 27, using
- base change [i] based on digital (7, 54, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 54, 172)-net over F81, using
(25, 49, 452)-Net over F27 — Digital
Digital (25, 49, 452)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2749, 452, F27, 24) (dual of [452, 403, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2749, 737, F27, 24) (dual of [737, 688, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(2747, 729, F27, 24) (dual of [729, 682, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2741, 729, F27, 21) (dual of [729, 688, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2749, 737, F27, 24) (dual of [737, 688, 25]-code), using
(25, 49, 142267)-Net in Base 27 — Upper bound on s
There is no (25, 49, 142268)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 13704 030032 857461 816370 760161 542017 084758 908138 770292 679353 478775 886657 > 2749 [i]