Best Known (22, 22+20, s)-Nets in Base 25
(22, 22+20, 156)-Net over F25 — Constructive and digital
Digital (22, 42, 156)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (9, 29, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (3, 13, 52)-net over F25, using
(22, 22+20, 473)-Net over F25 — Digital
Digital (22, 42, 473)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2542, 473, F25, 20) (dual of [473, 431, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2542, 636, F25, 20) (dual of [636, 594, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(2539, 625, F25, 20) (dual of [625, 586, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2531, 625, F25, 16) (dual of [625, 594, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(19) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(2542, 636, F25, 20) (dual of [636, 594, 21]-code), using
(22, 22+20, 140312)-Net in Base 25 — Upper bound on s
There is no (22, 42, 140313)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 51698 823835 091321 991909 928573 748819 410884 545034 757738 549681 > 2542 [i]