Best Known (26, 26+15, s)-Nets in Base 32
(26, 26+15, 363)-Net over F32 — Constructive and digital
Digital (26, 41, 363)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- 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, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 7, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 15, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 1, 33)-net over F32, using
(26, 26+15, 2340)-Net in Base 32 — Constructive
(26, 41, 2340)-net in base 32, using
- net defined by OOA [i] based on OOA(3241, 2340, S32, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3241, 16381, S32, 15), using
- discarding factors based on OA(3241, 16386, S32, 15), using
- discarding parts of the base [i] based on linear OA(12829, 16386, F128, 15) (dual of [16386, 16357, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(14) ⊂ Ce(13) [i] based on
- discarding parts of the base [i] based on linear OA(12829, 16386, F128, 15) (dual of [16386, 16357, 16]-code), using
- discarding factors based on OA(3241, 16386, S32, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3241, 16381, S32, 15), using
(26, 26+15, 4996)-Net over F32 — Digital
Digital (26, 41, 4996)-net over F32, using
(26, 26+15, large)-Net in Base 32 — Upper bound on s
There is no (26, 41, large)-net in base 32, because
- 13 times m-reduction [i] would yield (26, 28, large)-net in base 32, but