Best Known (61, 61+17, s)-Nets in Base 25
(61, 61+17, 48895)-Net over F25 — Constructive and digital
Digital (61, 78, 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 (49, 66, 48829)-net over F25, using
- net defined by OOA [i] based on linear OOA(2566, 48829, F25, 17, 17) (dual of [(48829, 17), 830027, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2566, 390633, F25, 17) (dual of [390633, 390567, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, 390635, F25, 17) (dual of [390635, 390569, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(2565, 390626, F25, 17) (dual of [390626, 390561, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2557, 390626, F25, 15) (dual of [390626, 390569, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [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 C([0,8]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2566, 390635, F25, 17) (dual of [390635, 390569, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2566, 390633, F25, 17) (dual of [390633, 390567, 18]-code), using
- net defined by OOA [i] based on linear OOA(2566, 48829, F25, 17, 17) (dual of [(48829, 17), 830027, 18]-NRT-code), using
- digital (4, 12, 66)-net over F25, using
(61, 61+17, 1850491)-Net over F25 — Digital
Digital (61, 78, 1850491)-net over F25, using
(61, 61+17, large)-Net in Base 25 — Upper bound on s
There is no (61, 78, large)-net in base 25, because
- 15 times m-reduction [i] would yield (61, 63, large)-net in base 25, but