Best Known (52−10, 52, s)-Nets in Base 32
(52−10, 52, 1677764)-Net over F32 — Constructive and digital
Digital (42, 52, 1677764)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 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 (36, 46, 1677720)-net over F32, using
- net defined by OOA [i] based on linear OOA(3246, 1677720, F32, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3246, 8388600, F32, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(3246, 8388600, F32, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(3246, 1677720, F32, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- digital (1, 6, 44)-net over F32, using
(52−10, 52, 1678216)-Net in Base 32 — Constructive
(42, 52, 1678216)-net in base 32, 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
- (35, 45, 1677720)-net in base 32, using
- net defined by OOA [i] based on OOA(3245, 1677720, S32, 10, 10), using
- OA 5-folding and stacking [i] based on OA(3245, 8388600, S32, 10), using
- discarding factors based on OA(3245, large, S32, 10), using
- discarding parts of the base [i] based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding parts of the base [i] based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- discarding factors based on OA(3245, large, S32, 10), using
- OA 5-folding and stacking [i] based on OA(3245, 8388600, S32, 10), using
- net defined by OOA [i] based on OOA(3245, 1677720, S32, 10, 10), using
- digital (2, 7, 496)-net over F32, using
(52−10, 52, large)-Net over F32 — Digital
Digital (42, 52, large)-net over F32, using
- 321 times duplication [i] based on digital (41, 51, large)-net over F32, using
- t-expansion [i] based on digital (40, 51, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] 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]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3251, large, F32, 11) (dual of [large, large−51, 12]-code), using
- t-expansion [i] based on digital (40, 51, large)-net over F32, using
(52−10, 52, large)-Net in Base 32 — Upper bound on s
There is no (42, 52, large)-net in base 32, because
- 8 times m-reduction [i] would yield (42, 44, large)-net in base 32, but