Best Known (26, 26+26, s)-Nets in Base 25
(26, 26+26, 200)-Net over F25 — Constructive and digital
Digital (26, 52, 200)-net over F25, using
- t-expansion [i] based on digital (25, 52, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
(26, 26+26, 371)-Net over F25 — Digital
Digital (26, 52, 371)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2552, 371, F25, 26) (dual of [371, 319, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2552, 634, F25, 26) (dual of [634, 582, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(2549, 625, F25, 26) (dual of [625, 576, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2543, 625, F25, 22) (dual of [625, 582, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(253, 9, F25, 3) (dual of [9, 6, 4]-code or 9-arc in PG(2,25) or 9-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(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2552, 634, F25, 26) (dual of [634, 582, 27]-code), using
(26, 26+26, 92241)-Net in Base 25 — Upper bound on s
There is no (26, 52, 92242)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 4 931050 372615 172193 711390 810460 061892 826869 020146 123581 620715 087072 906865 > 2552 [i]