Best Known (46, 46+10, s)-Nets in Base 25
(46, 46+10, 1678370)-Net over F25 — Constructive and digital
Digital (46, 56, 1678370)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (5, 10, 650)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 26)-net over F25, using
- s-reduction based on digital (0, 0, s)-net over F25 with arbitrarily large s, using
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 1, 26)-net over F25, using
- s-reduction based on digital (0, 1, s)-net over F25 with arbitrarily large s, using
- digital (0, 1, 26)-net over F25 (see above)
- digital (0, 1, 26)-net over F25 (see above)
- digital (0, 2, 26)-net over F25, using
- digital (0, 5, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (0, 0, 26)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (36, 46, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- digital (5, 10, 650)-net over F25, using
(46, 46+10, large)-Net over F25 — Digital
Digital (46, 56, large)-net over F25, using
- t-expansion [i] based on digital (44, 56, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
(46, 46+10, large)-Net in Base 25 — Upper bound on s
There is no (46, 56, large)-net in base 25, because
- 8 times m-reduction [i] would yield (46, 48, large)-net in base 25, but