Best Known (47, 58, s)-Nets in Base 32
(47, 58, 1678216)-Net over F32 — Constructive and digital
Digital (47, 58, 1678216)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- digital (40, 51, 1677720)-net over F32, using
- net defined by OOA [i] based on linear OOA(3251, 1677720, F32, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3251, 8388601, F32, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3251, large, F32, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3251, large, F32, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3251, 8388601, F32, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(3251, 1677720, F32, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- digital (2, 7, 496)-net over F32, using
(47, 58, large)-Net over F32 — Digital
Digital (47, 58, large)-net over F32, using
- 322 times duplication [i] based on digital (45, 56, large)-net over F32, using
- t-expansion [i] based on digital (44, 56, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3256, large, F32, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3256, large, F32, 12) (dual of [large, large−56, 13]-code), using
- t-expansion [i] based on digital (44, 56, large)-net over F32, using
(47, 58, large)-Net in Base 32 — Upper bound on s
There is no (47, 58, large)-net in base 32, because
- 9 times m-reduction [i] would yield (47, 49, large)-net in base 32, but