Best Known (74−16, 74, s)-Nets in Base 25
(74−16, 74, 48895)-Net over F25 — Constructive and digital
Digital (58, 74, 48895)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (46, 62, 48829)-net over F25, using
- net defined by OOA [i] based on linear OOA(2562, 48829, F25, 16, 16) (dual of [(48829, 16), 781202, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2562, 390632, F25, 16) (dual of [390632, 390570, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2562, 390634, F25, 16) (dual of [390634, 390572, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] 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]
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2562, 390634, F25, 16) (dual of [390634, 390572, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2562, 390632, F25, 16) (dual of [390632, 390570, 17]-code), using
- net defined by OOA [i] based on linear OOA(2562, 48829, F25, 16, 16) (dual of [(48829, 16), 781202, 17]-NRT-code), using
- digital (4, 12, 66)-net over F25, using
(74−16, 74, 2108924)-Net over F25 — Digital
Digital (58, 74, 2108924)-net over F25, using
(74−16, 74, large)-Net in Base 25 — Upper bound on s
There is no (58, 74, large)-net in base 25, because
- 14 times m-reduction [i] would yield (58, 60, large)-net in base 25, but