Best Known (38−18, 38, s)-Nets in Base 25
(38−18, 38, 153)-Net over F25 — Constructive and digital
Digital (20, 38, 153)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (10, 28, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (1, 10, 27)-net over F25, using
(38−18, 38, 477)-Net over F25 — Digital
Digital (20, 38, 477)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2538, 477, F25, 18) (dual of [477, 439, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2538, 636, F25, 18) (dual of [636, 598, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(2535, 625, F25, 18) (dual of [625, 590, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2527, 625, F25, 14) (dual of [625, 598, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(17) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2538, 636, F25, 18) (dual of [636, 598, 19]-code), using
(38−18, 38, 138019)-Net in Base 25 — Upper bound on s
There is no (20, 38, 138020)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 132354 967209 748133 950794 969473 361193 517027 378495 692897 > 2538 [i]