Best Known (51, 65, s)-Nets in Base 32
(51, 65, 149896)-Net over F32 — Constructive and digital
Digital (51, 65, 149896)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 12, 99)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 7, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- generalized (u, u+v)-construction [i] based on
- digital (39, 53, 149797)-net over F32, using
- net defined by OOA [i] based on linear OOA(3253, 149797, F32, 14, 14) (dual of [(149797, 14), 2097105, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3253, 1048579, F32, 14) (dual of [1048579, 1048526, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3253, 1048580, F32, 14) (dual of [1048580, 1048527, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(3253, 1048576, F32, 14) (dual of [1048576, 1048523, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3249, 1048576, F32, 13) (dual of [1048576, 1048527, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3253, 1048580, F32, 14) (dual of [1048580, 1048527, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3253, 1048579, F32, 14) (dual of [1048579, 1048526, 15]-code), using
- net defined by OOA [i] based on linear OOA(3253, 149797, F32, 14, 14) (dual of [(149797, 14), 2097105, 15]-NRT-code), using
- digital (5, 12, 99)-net over F32, using
(51, 65, 1198371)-Net in Base 32 — Constructive
(51, 65, 1198371)-net in base 32, using
- 321 times duplication [i] based on (50, 64, 1198371)-net in base 32, using
- base change [i] based on digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- base change [i] based on digital (26, 40, 1198371)-net over F256, using
(51, 65, 6134721)-Net over F32 — Digital
Digital (51, 65, 6134721)-net over F32, using
(51, 65, large)-Net in Base 32 — Upper bound on s
There is no (51, 65, large)-net in base 32, because
- 12 times m-reduction [i] would yield (51, 53, large)-net in base 32, but