Best Known (33, 51, s)-Nets in Base 32
(33, 51, 363)-Net over F32 — Constructive and digital
Digital (33, 51, 363)-net over F32, using
- 1 times m-reduction [i] based on digital (33, 52, 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, 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, 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, 6, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 9, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 19, 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, 51, 1821)-Net in Base 32 — Constructive
(33, 51, 1821)-net in base 32, using
- net defined by OOA [i] based on OOA(3251, 1821, S32, 18, 18), using
- OA 9-folding and stacking [i] based on OA(3251, 16389, S32, 18), using
- discarding parts of the base [i] based on linear OA(12836, 16389, F128, 18) (dual of [16389, 16353, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(12836, 16389, F128, 18) (dual of [16389, 16353, 19]-code), using
- OA 9-folding and stacking [i] based on OA(3251, 16389, S32, 18), using
(33, 51, 7595)-Net over F32 — Digital
Digital (33, 51, 7595)-net over F32, using
(33, 51, large)-Net in Base 32 — Upper bound on s
There is no (33, 51, large)-net in base 32, because
- 16 times m-reduction [i] would yield (33, 35, large)-net in base 32, but