Best Known (46, 63, s)-Nets in Base 256
(46, 63, 1049346)-Net over F256 — Constructive and digital
Digital (46, 63, 1049346)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 771)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 257)-net over F256, using
- digital (0, 4, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- digital (0, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- generalized (u, u+v)-construction [i] based on
- digital (32, 49, 1048575)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 1048575, F256, 17, 17) (dual of [(1048575, 17), 17825726, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25649, 8388601, F256, 17) (dual of [8388601, 8388552, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25649, 8388601, F256, 17) (dual of [8388601, 8388552, 18]-code), using
- net defined by OOA [i] based on linear OOA(25649, 1048575, F256, 17, 17) (dual of [(1048575, 17), 17825726, 18]-NRT-code), using
- digital (6, 14, 771)-net over F256, using
(46, 63, large)-Net over F256 — Digital
Digital (46, 63, large)-net over F256, using
- t-expansion [i] based on digital (45, 63, large)-net over F256, using
- 2 times m-reduction [i] based on digital (45, 65, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25665, large, F256, 20) (dual of [large, large−65, 21]-code), using
- 7 times code embedding in larger space [i] based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 7 times code embedding in larger space [i] based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25665, large, F256, 20) (dual of [large, large−65, 21]-code), using
- 2 times m-reduction [i] based on digital (45, 65, large)-net over F256, using
(46, 63, large)-Net in Base 256 — Upper bound on s
There is no (46, 63, large)-net in base 256, because
- 15 times m-reduction [i] would yield (46, 48, large)-net in base 256, but