Best Known (81−23, 81, s)-Nets in Base 25
(81−23, 81, 1472)-Net over F25 — Constructive and digital
Digital (58, 81, 1472)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (44, 67, 1420)-net over F25, using
- net defined by OOA [i] based on linear OOA(2567, 1420, F25, 23, 23) (dual of [(1420, 23), 32593, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2567, 15621, F25, 23) (dual of [15621, 15554, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2567, 15621, F25, 23) (dual of [15621, 15554, 24]-code), using
- net defined by OOA [i] based on linear OOA(2567, 1420, F25, 23, 23) (dual of [(1420, 23), 32593, 24]-NRT-code), using
- digital (3, 14, 52)-net over F25, using
(81−23, 81, 52929)-Net over F25 — Digital
Digital (58, 81, 52929)-net over F25, using
(81−23, 81, large)-Net in Base 25 — Upper bound on s
There is no (58, 81, large)-net in base 25, because
- 21 times m-reduction [i] would yield (58, 60, large)-net in base 25, but