Best Known (50−11, 50, s)-Nets in Base 32
(50−11, 50, 210244)-Net over F32 — Constructive and digital
Digital (39, 50, 210244)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (4, 9, 529)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- 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
- (u, u+v)-construction [i] based on
- digital (30, 41, 209715)-net over F32, using
- net defined by OOA [i] based on linear OOA(3241, 209715, F32, 11, 11) (dual of [(209715, 11), 2306824, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using
- net defined by OOA [i] based on linear OOA(3241, 209715, F32, 11, 11) (dual of [(209715, 11), 2306824, 12]-NRT-code), using
- digital (4, 9, 529)-net over F32, using
(50−11, 50, 1677720)-Net in Base 32 — Constructive
(39, 50, 1677720)-net in base 32, using
- net defined by OOA [i] based on OOA(3250, 1677720, S32, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(3250, 8388601, S32, 11), using
- discarding factors based on OA(3250, large, S32, 11), using
- discarding parts of the base [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- discarding factors based on OA(3250, large, S32, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(3250, 8388601, S32, 11), using
(50−11, 50, 4901906)-Net over F32 — Digital
Digital (39, 50, 4901906)-net over F32, using
(50−11, 50, large)-Net in Base 32 — Upper bound on s
There is no (39, 50, large)-net in base 32, because
- 9 times m-reduction [i] would yield (39, 41, large)-net in base 32, but