Best Known (74, 95, s)-Nets in Base 25
(74, 95, 39128)-Net over F25 — Constructive and digital
Digital (74, 95, 39128)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (60, 81, 39062)-net over F25, using
- net defined by OOA [i] based on linear OOA(2581, 39062, F25, 21, 21) (dual of [(39062, 21), 820221, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2581, 390621, F25, 21) (dual of [390621, 390540, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2581, 390625, F25, 21) (dual of [390625, 390544, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2581, 390625, F25, 21) (dual of [390625, 390544, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2581, 390621, F25, 21) (dual of [390621, 390540, 22]-code), using
- net defined by OOA [i] based on linear OOA(2581, 39062, F25, 21, 21) (dual of [(39062, 21), 820221, 22]-NRT-code), using
- digital (4, 14, 66)-net over F25, using
(74, 95, 1511169)-Net over F25 — Digital
Digital (74, 95, 1511169)-net over F25, using
(74, 95, large)-Net in Base 25 — Upper bound on s
There is no (74, 95, large)-net in base 25, because
- 19 times m-reduction [i] would yield (74, 76, large)-net in base 25, but