Best Known (36−13, 36, s)-Nets in Base 32
(36−13, 36, 396)-Net over F32 — Constructive and digital
Digital (23, 36, 396)-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, 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, 4, 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, 13, 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
(36−13, 36, 2731)-Net in Base 32 — Constructive
(23, 36, 2731)-net in base 32, using
- net defined by OOA [i] based on OOA(3236, 2731, S32, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(3236, 16387, S32, 13), using
- 1 times code embedding in larger space [i] based on OA(3235, 16386, S32, 13), using
- discarding parts of the base [i] based on linear OA(12825, 16386, F128, 13) (dual of [16386, 16361, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- 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(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- discarding parts of the base [i] based on linear OA(12825, 16386, F128, 13) (dual of [16386, 16361, 14]-code), using
- 1 times code embedding in larger space [i] based on OA(3235, 16386, S32, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(3236, 16387, S32, 13), using
(36−13, 36, 5596)-Net over F32 — Digital
Digital (23, 36, 5596)-net over F32, using
(36−13, 36, large)-Net in Base 32 — Upper bound on s
There is no (23, 36, large)-net in base 32, because
- 11 times m-reduction [i] would yield (23, 25, large)-net in base 32, but