Best Known (72−26, 72, s)-Nets in Base 32
(72−26, 72, 330)-Net over F32 — Constructive and digital
Digital (46, 72, 330)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- 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, 3, 33)-net over F32 (see above)
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 6, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 8, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 13, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 26, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
(72−26, 72, 1260)-Net in Base 32 — Constructive
(46, 72, 1260)-net in base 32, using
- net defined by OOA [i] based on OOA(3272, 1260, S32, 26, 26), using
- OA 13-folding and stacking [i] based on OA(3272, 16380, S32, 26), using
- discarding factors based on OA(3272, 16386, S32, 26), using
- discarding parts of the base [i] based on linear OA(12851, 16386, F128, 26) (dual of [16386, 16335, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(12851, 16384, F128, 26) (dual of [16384, 16333, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(12849, 16384, F128, 25) (dual of [16384, 16335, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- discarding parts of the base [i] based on linear OA(12851, 16386, F128, 26) (dual of [16386, 16335, 27]-code), using
- discarding factors based on OA(3272, 16386, S32, 26), using
- OA 13-folding and stacking [i] based on OA(3272, 16380, S32, 26), using
(72−26, 72, 7110)-Net over F32 — Digital
Digital (46, 72, 7110)-net over F32, using
(72−26, 72, large)-Net in Base 32 — Upper bound on s
There is no (46, 72, large)-net in base 32, because
- 24 times m-reduction [i] would yield (46, 48, large)-net in base 32, but