Best Known (52−28, 52, s)-Nets in Base 25
(52−28, 52, 152)-Net over F25 — Constructive and digital
Digital (24, 52, 152)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (10, 38, 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 (0, 14, 26)-net over F25, using
(52−28, 52, 253)-Net over F25 — Digital
Digital (24, 52, 253)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2552, 253, F25, 2, 28) (dual of [(253, 2), 454, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2552, 313, F25, 2, 28) (dual of [(313, 2), 574, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2552, 626, F25, 28) (dual of [626, 574, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2552, 627, F25, 28) (dual of [627, 575, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(2552, 625, F25, 28) (dual of [625, 573, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2550, 625, F25, 27) (dual of [625, 575, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2552, 627, F25, 28) (dual of [627, 575, 29]-code), using
- OOA 2-folding [i] based on linear OA(2552, 626, F25, 28) (dual of [626, 574, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(2552, 313, F25, 2, 28) (dual of [(313, 2), 574, 29]-NRT-code), using
(52−28, 52, 39220)-Net in Base 25 — Upper bound on s
There is no (24, 52, 39221)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 4 930696 068798 828584 761013 594550 202615 922857 105828 883816 515523 114005 131985 > 2552 [i]