Best Known (33−12, 33, s)-Nets in Base 32
(33−12, 33, 330)-Net over F32 — Constructive and digital
Digital (21, 33, 330)-net over F32, using
- 1 times m-reduction [i] based on digital (21, 34, 330)-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, 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
- generalized (u, u+v)-construction [i] based on
(33−12, 33, 2731)-Net in Base 32 — Constructive
(21, 33, 2731)-net in base 32, using
- net defined by OOA [i] based on OOA(3233, 2731, S32, 12, 12), using
- OA 6-folding and stacking [i] based on OA(3233, 16386, S32, 12), using
- discarding parts of the base [i] based on linear OA(12823, 16386, F128, 12) (dual of [16386, 16363, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- 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(12821, 16384, F128, 11) (dual of [16384, 16363, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- discarding parts of the base [i] based on linear OA(12823, 16386, F128, 12) (dual of [16386, 16363, 13]-code), using
- OA 6-folding and stacking [i] based on OA(3233, 16386, S32, 12), using
(33−12, 33, 5195)-Net over F32 — Digital
Digital (21, 33, 5195)-net over F32, using
(33−12, 33, large)-Net in Base 32 — Upper bound on s
There is no (21, 33, large)-net in base 32, because
- 10 times m-reduction [i] would yield (21, 23, large)-net in base 32, but