Best Known (77, 110, s)-Nets in Base 25
(77, 110, 1002)-Net over F25 — Constructive and digital
Digital (77, 110, 1002)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 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 (61, 94, 976)-net over F25, using
- net defined by OOA [i] based on linear OOA(2594, 976, F25, 33, 33) (dual of [(976, 33), 32114, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(2594, 15617, F25, 33) (dual of [15617, 15523, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2594, 15625, F25, 33) (dual of [15625, 15531, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- discarding factors / shortening the dual code based on linear OA(2594, 15625, F25, 33) (dual of [15625, 15531, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(2594, 15617, F25, 33) (dual of [15617, 15523, 34]-code), using
- net defined by OOA [i] based on linear OOA(2594, 976, F25, 33, 33) (dual of [(976, 33), 32114, 34]-NRT-code), using
- digital (0, 16, 26)-net over F25, using
(77, 110, 34064)-Net over F25 — Digital
Digital (77, 110, 34064)-net over F25, using
(77, 110, large)-Net in Base 25 — Upper bound on s
There is no (77, 110, large)-net in base 25, because
- 31 times m-reduction [i] would yield (77, 79, large)-net in base 25, but