Best Known (92−16, 92, s)-Nets in Base 32
(92−16, 92, 1048832)-Net over F32 — Constructive and digital
Digital (76, 92, 1048832)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (8, 16, 257)-net over F32, using
- net defined by OOA [i] based on linear OOA(3216, 257, F32, 8, 8) (dual of [(257, 8), 2040, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3216, 1028, F32, 8) (dual of [1028, 1012, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, 1029, F32, 8) (dual of [1029, 1013, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [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]
- linear OA(3211, 1024, F32, 6) (dual of [1024, 1013, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(3216, 1029, F32, 8) (dual of [1029, 1013, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(3216, 1028, F32, 8) (dual of [1028, 1012, 9]-code), using
- net defined by OOA [i] based on linear OOA(3216, 257, F32, 8, 8) (dual of [(257, 8), 2040, 9]-NRT-code), using
- digital (60, 76, 1048575)-net over F32, using
- net defined by OOA [i] based on linear OOA(3276, 1048575, F32, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3276, 8388600, F32, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3276, 8388600, F32, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(3276, 1048575, F32, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- digital (8, 16, 257)-net over F32, using
(92−16, 92, 1049599)-Net in Base 32 — Constructive
(76, 92, 1049599)-net in base 32, using
- (u, u+v)-construction [i] based on
- (10, 18, 1024)-net in base 32, using
- base change [i] based on digital (7, 15, 1024)-net over F64, using
- net defined by OOA [i] based on linear OOA(6415, 1024, F64, 8, 8) (dual of [(1024, 8), 8177, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using
- net defined by OOA [i] based on linear OOA(6415, 1024, F64, 8, 8) (dual of [(1024, 8), 8177, 9]-NRT-code), using
- base change [i] based on digital (7, 15, 1024)-net over F64, using
- (58, 74, 1048575)-net in base 32, using
- net defined by OOA [i] based on OOA(3274, 1048575, S32, 16, 16), using
- OA 8-folding and stacking [i] based on OA(3274, 8388600, S32, 16), using
- discarding factors based on OA(3274, large, S32, 16), using
- discarding parts of the base [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding parts of the base [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- discarding factors based on OA(3274, large, S32, 16), using
- OA 8-folding and stacking [i] based on OA(3274, 8388600, S32, 16), using
- net defined by OOA [i] based on OOA(3274, 1048575, S32, 16, 16), using
- (10, 18, 1024)-net in base 32, using
(92−16, 92, large)-Net over F32 — Digital
Digital (76, 92, large)-net over F32, using
- t-expansion [i] based on digital (75, 92, large)-net over F32, using
- 3 times m-reduction [i] based on digital (75, 95, large)-net over F32, using
(92−16, 92, large)-Net in Base 32 — Upper bound on s
There is no (76, 92, large)-net in base 32, because
- 14 times m-reduction [i] would yield (76, 78, large)-net in base 32, but