Best Known (63, 63+19, s)-Nets in Base 25
(63, 63+19, 43429)-Net over F25 — Constructive and digital
Digital (63, 82, 43429)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (54, 73, 43403)-net over F25, using
- net defined by OOA [i] based on linear OOA(2573, 43403, F25, 19, 19) (dual of [(43403, 19), 824584, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2573, 390628, F25, 19) (dual of [390628, 390555, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2573, 390629, F25, 19) (dual of [390629, 390556, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(2573, 390625, F25, 19) (dual of [390625, 390552, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2569, 390625, F25, 18) (dual of [390625, 390556, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 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(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(2573, 390629, F25, 19) (dual of [390629, 390556, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2573, 390628, F25, 19) (dual of [390628, 390555, 20]-code), using
- net defined by OOA [i] based on linear OOA(2573, 43403, F25, 19, 19) (dual of [(43403, 19), 824584, 20]-NRT-code), using
- digital (0, 9, 26)-net over F25, using
(63, 63+19, 735051)-Net over F25 — Digital
Digital (63, 82, 735051)-net over F25, using
(63, 63+19, large)-Net in Base 25 — Upper bound on s
There is no (63, 82, large)-net in base 25, because
- 17 times m-reduction [i] would yield (63, 65, large)-net in base 25, but