Best Known (26−12, 26, s)-Nets in Base 25
(26−12, 26, 132)-Net over F25 — Constructive and digital
Digital (14, 26, 132)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (4, 16, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25 (see above)
- digital (4, 10, 66)-net over F25, using
(26−12, 26, 585)-Net over F25 — Digital
Digital (14, 26, 585)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2526, 585, F25, 12) (dual of [585, 559, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2526, 636, F25, 12) (dual of [636, 610, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(2523, 625, F25, 12) (dual of [625, 602, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2515, 625, F25, 8) (dual of [625, 610, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(2526, 636, F25, 12) (dual of [636, 610, 13]-code), using
(26−12, 26, 142476)-Net in Base 25 — Upper bound on s
There is no (14, 26, 142477)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2 220515 556649 033769 997930 835489 728145 > 2526 [i]