Best Known (33, 33+8, s)-Nets in Base 32
(33, 33+8, 2097194)-Net over F32 — Constructive and digital
Digital (33, 41, 2097194)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (28, 36, 2097150)-net over F32, using
- net defined by OOA [i] based on linear OOA(3236, 2097150, F32, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3236, 8388600, F32, 8) (dual of [8388600, 8388564, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, large, F32, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(3236, large, F32, 8) (dual of [large, large−36, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(3236, 8388600, F32, 8) (dual of [8388600, 8388564, 9]-code), using
- net defined by OOA [i] based on linear OOA(3236, 2097150, F32, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- digital (1, 5, 44)-net over F32, using
(33, 33+8, 2097646)-Net in Base 32 — Constructive
(33, 41, 2097646)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(326, 496, F32, 4, 4) (dual of [(496, 4), 1978, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
- 1 times truncation [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
- net defined by OOA [i] based on linear OOA(326, 496, F32, 4, 4) (dual of [(496, 4), 1978, 5]-NRT-code), using
- (27, 35, 2097150)-net in base 32, using
- net defined by OOA [i] based on OOA(3235, 2097150, S32, 8, 8), using
- OA 4-folding and stacking [i] based on OA(3235, 8388600, S32, 8), using
- discarding factors based on OA(3235, large, S32, 8), using
- discarding parts of the base [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding parts of the base [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- discarding factors based on OA(3235, large, S32, 8), using
- OA 4-folding and stacking [i] based on OA(3235, 8388600, S32, 8), using
- net defined by OOA [i] based on OOA(3235, 2097150, S32, 8, 8), using
- digital (2, 6, 496)-net over F32, using
(33, 33+8, large)-Net over F32 — Digital
Digital (33, 41, large)-net over F32, using
- t-expansion [i] based on digital (32, 41, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
(33, 33+8, large)-Net in Base 32 — Upper bound on s
There is no (33, 41, large)-net in base 32, because
- 6 times m-reduction [i] would yield (33, 35, large)-net in base 32, but