Best Known (23, 33, s)-Nets in Base 25
(23, 33, 3151)-Net over F25 — Constructive and digital
Digital (23, 33, 3151)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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 (18, 28, 3125)-net over F25, using
- net defined by OOA [i] based on linear OOA(2528, 3125, F25, 10, 10) (dual of [(3125, 10), 31222, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- OA 5-folding and stacking [i] based on linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using
- net defined by OOA [i] based on linear OOA(2528, 3125, F25, 10, 10) (dual of [(3125, 10), 31222, 11]-NRT-code), using
- digital (0, 5, 26)-net over F25, using
(23, 33, 23089)-Net over F25 — Digital
Digital (23, 33, 23089)-net over F25, using
(23, 33, large)-Net in Base 25 — Upper bound on s
There is no (23, 33, large)-net in base 25, because
- 8 times m-reduction [i] would yield (23, 25, large)-net in base 25, but