Best Known (102−32, 102, s)-Nets in Base 32
(102−32, 102, 2050)-Net over F32 — Constructive and digital
Digital (70, 102, 2050)-net over F32, using
- net defined by OOA [i] based on linear OOA(32102, 2050, F32, 32, 32) (dual of [(2050, 32), 65498, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(32102, 32800, F32, 32) (dual of [32800, 32698, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(32102, 32801, F32, 32) (dual of [32801, 32699, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(22) [i] based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(328, 33, F32, 8) (dual of [33, 25, 9]-code or 33-arc in PG(7,32)), using
- extended Reed–Solomon code RSe(25,32) [i]
- construction X applied to Ce(32) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(32102, 32801, F32, 32) (dual of [32801, 32699, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(32102, 32800, F32, 32) (dual of [32800, 32698, 33]-code), using
(102−32, 102, 4096)-Net in Base 32 — Constructive
(70, 102, 4096)-net in base 32, using
- base change [i] based on (53, 85, 4096)-net in base 64, using
- 641 times duplication [i] based on (52, 84, 4096)-net in base 64, using
- base change [i] based on digital (31, 63, 4096)-net over F256, using
- net defined by OOA [i] based on linear OOA(25663, 4096, F256, 32, 32) (dual of [(4096, 32), 131009, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(25663, 65536, F256, 32) (dual of [65536, 65473, 33]-code), using
- an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- OA 16-folding and stacking [i] based on linear OA(25663, 65536, F256, 32) (dual of [65536, 65473, 33]-code), using
- net defined by OOA [i] based on linear OOA(25663, 4096, F256, 32, 32) (dual of [(4096, 32), 131009, 33]-NRT-code), using
- base change [i] based on digital (31, 63, 4096)-net over F256, using
- 641 times duplication [i] based on (52, 84, 4096)-net in base 64, using
(102−32, 102, 35916)-Net over F32 — Digital
Digital (70, 102, 35916)-net over F32, using
(102−32, 102, large)-Net in Base 32 — Upper bound on s
There is no (70, 102, large)-net in base 32, because
- 30 times m-reduction [i] would yield (70, 72, large)-net in base 32, but