Best Known (80, 92, s)-Nets in Base 32
(80, 92, 2812585)-Net over F32 — Constructive and digital
Digital (80, 92, 2812585)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 10, 16385)-net over F32, using
- net defined by OOA [i] based on linear OOA(3210, 16385, F32, 4, 4) (dual of [(16385, 4), 65530, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(3210, 32770, F32, 4) (dual of [32770, 32760, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- 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(327, 32768, F32, 3) (dual of [32768, 32761, 4]-code or 32768-cap in PG(6,32)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(3210, 32770, F32, 4) (dual of [32770, 32760, 5]-code), using
- net defined by OOA [i] based on linear OOA(3210, 16385, F32, 4, 4) (dual of [(16385, 4), 65530, 5]-NRT-code), using
- digital (20, 26, 1398100)-net over F32, using
- s-reduction based on digital (20, 26, 2796201)-net over F32, using
- net defined by OOA [i] based on linear OOA(3226, 2796201, F32, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(3226, 2796201, F32, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- s-reduction based on digital (20, 26, 2796201)-net over F32, 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 (6, 10, 16385)-net over F32, using
(80, 92, 2828840)-Net in Base 32 — Constructive
(80, 92, 2828840)-net in base 32, using
- 321 times duplication [i] based on (79, 91, 2828840)-net in base 32, using
- base change [i] based on (53, 65, 2828840)-net in base 128, using
- 1281 times duplication [i] based on (52, 64, 2828840)-net in base 128, using
- base change [i] based on digital (44, 56, 2828840)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 6, 32640)-net over F256, using
- net defined by OOA [i] based on linear OOA(2566, 32640, F256, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- 1 times truncation [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- net defined by OOA [i] based on linear OOA(2566, 32640, F256, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
- digital (10, 16, 1398100)-net over F256, using
- s-reduction based on digital (10, 16, 2796201)-net over F256, using
- net defined by OOA [i] based on linear OOA(25616, 2796201, F256, 6, 6) (dual of [(2796201, 6), 16777190, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- net defined by OOA [i] based on linear OOA(25616, 2796201, F256, 6, 6) (dual of [(2796201, 6), 16777190, 7]-NRT-code), using
- s-reduction based on digital (10, 16, 2796201)-net over F256, 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 (2, 6, 32640)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- base change [i] based on digital (44, 56, 2828840)-net over F256, using
- 1281 times duplication [i] based on (52, 64, 2828840)-net in base 128, using
- base change [i] based on (53, 65, 2828840)-net in base 128, using
(80, 92, large)-Net over F32 — Digital
Digital (80, 92, large)-net over F32, using
- t-expansion [i] based on digital (79, 92, large)-net over F32, using
- 8 times m-reduction [i] based on digital (79, 100, large)-net over F32, using
(80, 92, large)-Net in Base 32 — Upper bound on s
There is no (80, 92, large)-net in base 32, because
- 10 times m-reduction [i] would yield (80, 82, large)-net in base 32, but