Best Known (73−12, 73, s)-Nets in Base 32
(73−12, 73, 1409025)-Net over F32 — Constructive and digital
Digital (61, 73, 1409025)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 17, 10925)-net over F32, using
- net defined by OOA [i] based on linear OOA(3217, 10925, F32, 6, 6) (dual of [(10925, 6), 65533, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3217, 32775, F32, 6) (dual of [32775, 32758, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(3216, 32768, F32, 6) (dual of [32768, 32752, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 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(5) ⊂ Ce(3) [i] based on
- OA 3-folding and stacking [i] based on linear OA(3217, 32775, F32, 6) (dual of [32775, 32758, 7]-code), using
- net defined by OOA [i] based on linear OOA(3217, 10925, F32, 6, 6) (dual of [(10925, 6), 65533, 7]-NRT-code), using
- digital (44, 56, 1398100)-net over F32, using
- net defined by OOA [i] based on linear OOA(3256, 1398100, F32, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3256, 8388600, F32, 12) (dual of [8388600, 8388544, 13]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(3256, large, F32, 12) (dual of [large, large−56, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3256, 8388600, F32, 12) (dual of [8388600, 8388544, 13]-code), using
- net defined by OOA [i] based on linear OOA(3256, 1398100, F32, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- digital (11, 17, 10925)-net over F32, using
(73−12, 73, 1419946)-Net in Base 32 — Constructive
(61, 73, 1419946)-net in base 32, using
- 321 times duplication [i] based on (60, 72, 1419946)-net in base 32, using
- base change [i] based on digital (33, 45, 1419946)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (5, 11, 21846)-net over F256, using
- net defined by OOA [i] based on linear OOA(25611, 21846, F256, 6, 6) (dual of [(21846, 6), 131065, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25611, 65538, F256, 6) (dual of [65538, 65527, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2569, 65536, F256, 5) (dual of [65536, 65527, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(25611, 65538, F256, 6) (dual of [65538, 65527, 7]-code), using
- net defined by OOA [i] based on linear OOA(25611, 21846, F256, 6, 6) (dual of [(21846, 6), 131065, 7]-NRT-code), using
- digital (22, 34, 1398100)-net over F256, using
- net defined by OOA [i] based on linear OOA(25634, 1398100, F256, 12, 12) (dual of [(1398100, 12), 16777166, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- net defined by OOA [i] based on linear OOA(25634, 1398100, F256, 12, 12) (dual of [(1398100, 12), 16777166, 13]-NRT-code), using
- digital (5, 11, 21846)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (33, 45, 1419946)-net over F256, using
(73−12, 73, large)-Net over F32 — Digital
Digital (61, 73, large)-net over F32, using
- t-expansion [i] based on digital (60, 73, large)-net over F32, using
- 3 times m-reduction [i] based on digital (60, 76, large)-net over F32, using
(73−12, 73, large)-Net in Base 32 — Upper bound on s
There is no (61, 73, large)-net in base 32, because
- 10 times m-reduction [i] would yield (61, 63, large)-net in base 32, but