Best Known (55, 71, s)-Nets in Base 25
(55, 71, 48856)-Net over F25 — Constructive and digital
Digital (55, 71, 48856)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
- digital (45, 61, 48828)-net over F25, using
- net defined by OOA [i] based on linear OOA(2561, 48828, F25, 16, 16) (dual of [(48828, 16), 781187, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2561, 390624, F25, 16) (dual of [390624, 390563, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2561, 390624, F25, 16) (dual of [390624, 390563, 17]-code), using
- net defined by OOA [i] based on linear OOA(2561, 48828, F25, 16, 16) (dual of [(48828, 16), 781187, 17]-NRT-code), using
- digital (2, 10, 28)-net over F25, using
(55, 71, 1107833)-Net over F25 — Digital
Digital (55, 71, 1107833)-net over F25, using
(55, 71, large)-Net in Base 25 — Upper bound on s
There is no (55, 71, large)-net in base 25, because
- 14 times m-reduction [i] would yield (55, 57, large)-net in base 25, but