Best Known (65, 65+26, s)-Nets in Base 25
(65, 65+26, 1268)-Net over F25 — Constructive and digital
Digital (65, 91, 1268)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 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 (48, 74, 1202)-net over F25, using
- net defined by OOA [i] based on linear OOA(2574, 1202, F25, 26, 26) (dual of [(1202, 26), 31178, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2574, 15626, F25, 26) (dual of [15626, 15552, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2574, 15629, F25, 26) (dual of [15629, 15555, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(251, 4, F25, 1) (dual of [4, 3, 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(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(2574, 15629, F25, 26) (dual of [15629, 15555, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2574, 15626, F25, 26) (dual of [15626, 15552, 27]-code), using
- net defined by OOA [i] based on linear OOA(2574, 1202, F25, 26, 26) (dual of [(1202, 26), 31178, 27]-NRT-code), using
- digital (4, 17, 66)-net over F25, using
(65, 65+26, 52002)-Net over F25 — Digital
Digital (65, 91, 52002)-net over F25, using
(65, 65+26, large)-Net in Base 25 — Upper bound on s
There is no (65, 91, large)-net in base 25, because
- 24 times m-reduction [i] would yield (65, 67, large)-net in base 25, but