Best Known (47, 47+17, s)-Nets in Base 32
(47, 47+17, 4352)-Net over F32 — Constructive and digital
Digital (47, 64, 4352)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 15, 256)-net over F32, using
- net defined by OOA [i] based on linear OOA(3215, 256, F32, 8, 8) (dual of [(256, 8), 2033, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using
- net defined by OOA [i] based on linear OOA(3215, 256, F32, 8, 8) (dual of [(256, 8), 2033, 9]-NRT-code), using
- digital (32, 49, 4096)-net over F32, using
- net defined by OOA [i] based on linear OOA(3249, 4096, F32, 17, 17) (dual of [(4096, 17), 69583, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3249, 32769, F32, 17) (dual of [32769, 32720, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(3249, 32769, F32, 17) (dual of [32769, 32720, 18]-code), using
- net defined by OOA [i] based on linear OOA(3249, 4096, F32, 17, 17) (dual of [(4096, 17), 69583, 18]-NRT-code), using
- digital (7, 15, 256)-net over F32, using
(47, 47+17, 32770)-Net in Base 32 — Constructive
(47, 64, 32770)-net in base 32, using
- net defined by OOA [i] based on OOA(3264, 32770, S32, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3264, 262161, S32, 17), using
- discarding factors based on OA(3264, 262163, S32, 17), using
- discarding parts of the base [i] based on linear OA(6453, 262163, F64, 17) (dual of [262163, 262110, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(6449, 262144, F64, 17) (dual of [262144, 262095, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- discarding parts of the base [i] based on linear OA(6453, 262163, F64, 17) (dual of [262163, 262110, 18]-code), using
- discarding factors based on OA(3264, 262163, S32, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3264, 262161, S32, 17), using
(47, 47+17, 230034)-Net over F32 — Digital
Digital (47, 64, 230034)-net over F32, using
(47, 47+17, large)-Net in Base 32 — Upper bound on s
There is no (47, 64, large)-net in base 32, because
- 15 times m-reduction [i] would yield (47, 49, large)-net in base 32, but