Best Known (68, 68+26, s)-Nets in Base 25
(68, 68+26, 1269)-Net over F25 — Constructive and digital
Digital (68, 94, 1269)-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 (51, 77, 1203)-net over F25, using
- net defined by OOA [i] based on linear OOA(2577, 1203, F25, 26, 26) (dual of [(1203, 26), 31201, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2577, 15639, F25, 26) (dual of [15639, 15562, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2577, 15641, F25, 26) (dual of [15641, 15564, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [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(2561, 15625, F25, 21) (dual of [15625, 15564, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(254, 16, F25, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2577, 15641, F25, 26) (dual of [15641, 15564, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2577, 15639, F25, 26) (dual of [15639, 15562, 27]-code), using
- net defined by OOA [i] based on linear OOA(2577, 1203, F25, 26, 26) (dual of [(1203, 26), 31201, 27]-NRT-code), using
- digital (4, 17, 66)-net over F25, using
(68, 68+26, 76514)-Net over F25 — Digital
Digital (68, 94, 76514)-net over F25, using
(68, 68+26, large)-Net in Base 25 — Upper bound on s
There is no (68, 94, large)-net in base 25, because
- 24 times m-reduction [i] would yield (68, 70, large)-net in base 25, but