Best Known (78−22, 78, s)-Nets in Base 25
(78−22, 78, 1472)-Net over F25 — Constructive and digital
Digital (56, 78, 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 (42, 64, 1420)-net over F25, using
- net defined by OOA [i] based on linear OOA(2564, 1420, F25, 22, 22) (dual of [(1420, 22), 31176, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2564, 15620, F25, 22) (dual of [15620, 15556, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2564, 15620, F25, 22) (dual of [15620, 15556, 23]-code), using
- net defined by OOA [i] based on linear OOA(2564, 1420, F25, 22, 22) (dual of [(1420, 22), 31176, 23]-NRT-code), using
- digital (3, 14, 52)-net over F25, using
(78−22, 78, 56326)-Net over F25 — Digital
Digital (56, 78, 56326)-net over F25, using
(78−22, 78, large)-Net in Base 25 — Upper bound on s
There is no (56, 78, large)-net in base 25, because
- 20 times m-reduction [i] would yield (56, 58, large)-net in base 25, but