Best Known (38−14, 38, s)-Nets in Base 32
(38−14, 38, 363)-Net over F32 — Constructive and digital
Digital (24, 38, 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, 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, 4, 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, 14, 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
(38−14, 38, 2340)-Net in Base 32 — Constructive
(24, 38, 2340)-net in base 32, using
- net defined by OOA [i] based on OOA(3238, 2340, S32, 14, 14), using
- OA 7-folding and stacking [i] based on OA(3238, 16380, S32, 14), using
- discarding factors based on OA(3238, 16386, S32, 14), using
- discarding parts of the base [i] based on linear OA(12827, 16386, F128, 14) (dual of [16386, 16359, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- 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(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- discarding parts of the base [i] based on linear OA(12827, 16386, F128, 14) (dual of [16386, 16359, 15]-code), using
- discarding factors based on OA(3238, 16386, S32, 14), using
- OA 7-folding and stacking [i] based on OA(3238, 16380, S32, 14), using
(38−14, 38, 4595)-Net over F32 — Digital
Digital (24, 38, 4595)-net over F32, using
(38−14, 38, large)-Net in Base 32 — Upper bound on s
There is no (24, 38, large)-net in base 32, because
- 12 times m-reduction [i] would yield (24, 26, large)-net in base 32, but