Best Known (34, 34+14, s)-Nets in Base 25
(34, 34+14, 2259)-Net over F25 — Constructive and digital
Digital (34, 48, 2259)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (26, 40, 2232)-net over F25, using
- net defined by OOA [i] based on linear OOA(2540, 2232, F25, 14, 14) (dual of [(2232, 14), 31208, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2540, 15624, F25, 14) (dual of [15624, 15584, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2540, 15625, F25, 14) (dual of [15625, 15585, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(2540, 15625, F25, 14) (dual of [15625, 15585, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2540, 15624, F25, 14) (dual of [15624, 15584, 15]-code), using
- net defined by OOA [i] based on linear OOA(2540, 2232, F25, 14, 14) (dual of [(2232, 14), 31208, 15]-NRT-code), using
- digital (1, 8, 27)-net over F25, using
(34, 34+14, 34269)-Net over F25 — Digital
Digital (34, 48, 34269)-net over F25, using
(34, 34+14, large)-Net in Base 25 — Upper bound on s
There is no (34, 48, large)-net in base 25, because
- 12 times m-reduction [i] would yield (34, 36, large)-net in base 25, but