Best Known (77, 109, s)-Nets in Base 25
(77, 109, 1004)-Net over F25 — Constructive and digital
Digital (77, 109, 1004)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 18, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
- digital (59, 91, 976)-net over F25, using
- net defined by OOA [i] based on linear OOA(2591, 976, F25, 32, 32) (dual of [(976, 32), 31141, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(2591, 15616, F25, 32) (dual of [15616, 15525, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using
- an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- discarding factors / shortening the dual code based on linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(2591, 15616, F25, 32) (dual of [15616, 15525, 33]-code), using
- net defined by OOA [i] based on linear OOA(2591, 976, F25, 32, 32) (dual of [(976, 32), 31141, 33]-NRT-code), using
- digital (2, 18, 28)-net over F25, using
(77, 109, 42591)-Net over F25 — Digital
Digital (77, 109, 42591)-net over F25, using
(77, 109, large)-Net in Base 25 — Upper bound on s
There is no (77, 109, large)-net in base 25, because
- 30 times m-reduction [i] would yield (77, 79, large)-net in base 25, but