Best Known (54−12, 54, s)-Nets in Base 25
(54−12, 54, 65156)-Net over F25 — Constructive and digital
Digital (42, 54, 65156)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 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 (33, 45, 65104)-net over F25, using
- net defined by OOA [i] based on linear OOA(2545, 65104, F25, 12, 12) (dual of [(65104, 12), 781203, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2545, 390624, F25, 12) (dual of [390624, 390579, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2545, 390625, F25, 12) (dual of [390625, 390580, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(2545, 390625, F25, 12) (dual of [390625, 390580, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2545, 390624, F25, 12) (dual of [390624, 390579, 13]-code), using
- net defined by OOA [i] based on linear OOA(2545, 65104, F25, 12, 12) (dual of [(65104, 12), 781203, 13]-NRT-code), using
- digital (3, 9, 52)-net over F25, using
(54−12, 54, 1490799)-Net over F25 — Digital
Digital (42, 54, 1490799)-net over F25, using
(54−12, 54, large)-Net in Base 25 — Upper bound on s
There is no (42, 54, large)-net in base 25, because
- 10 times m-reduction [i] would yield (42, 44, large)-net in base 25, but