Best Known (43−8, 43, s)-Nets in Base 32
(43−8, 43, 2097663)-Net over F32 — Constructive and digital
Digital (35, 43, 2097663)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 7, 513)-net over F32, using
- net defined by OOA [i] based on linear OOA(327, 513, F32, 4, 4) (dual of [(513, 4), 2045, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(327, 1026, F32, 4) (dual of [1026, 1019, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(327, 1024, F32, 4) (dual of [1024, 1017, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(325, 1024, F32, 3) (dual of [1024, 1019, 4]-code or 1024-cap in PG(4,32)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- OA 2-folding and stacking [i] based on linear OA(327, 1026, F32, 4) (dual of [1026, 1019, 5]-code), using
- net defined by OOA [i] based on linear OOA(327, 513, F32, 4, 4) (dual of [(513, 4), 2045, 5]-NRT-code), 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 (3, 7, 513)-net over F32, using
(43−8, 43, 2099166)-Net in Base 32 — Constructive
(35, 43, 2099166)-net in base 32, using
- 321 times duplication [i] based on (34, 42, 2099166)-net in base 32, using
- base change [i] based on digital (27, 35, 2099166)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 2016)-net over F64, using
- net defined by OOA [i] based on linear OOA(646, 2016, F64, 4, 4) (dual of [(2016, 4), 8058, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(646, 2016, F64, 3, 4) (dual of [(2016, 3), 6042, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- 1 times truncation [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- appending kth column [i] based on linear OOA(646, 2016, F64, 3, 4) (dual of [(2016, 3), 6042, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(646, 2016, F64, 4, 4) (dual of [(2016, 4), 8058, 5]-NRT-code), using
- digital (21, 29, 2097150)-net over F64, using
- net defined by OOA [i] based on linear OOA(6429, 2097150, F64, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(6429, 8388600, F64, 8) (dual of [8388600, 8388571, 9]-code), using
- discarding factors / shortening the dual code 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 factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(6429, 8388600, F64, 8) (dual of [8388600, 8388571, 9]-code), using
- net defined by OOA [i] based on linear OOA(6429, 2097150, F64, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
- digital (2, 6, 2016)-net over F64, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (27, 35, 2099166)-net over F64, using
(43−8, 43, large)-Net over F32 — Digital
Digital (35, 43, large)-net over F32, using
- 322 times duplication [i] based on 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
- t-expansion [i] based on digital (32, 41, large)-net over F32, using
(43−8, 43, large)-Net in Base 32 — Upper bound on s
There is no (35, 43, large)-net in base 32, because
- 6 times m-reduction [i] would yield (35, 37, large)-net in base 32, but