Best Known (26, 40, s)-Nets in Base 32
(26, 40, 4681)-Net over F32 — Constructive and digital
Digital (26, 40, 4681)-net over F32, using
- net defined by OOA [i] based on linear OOA(3240, 4681, F32, 14, 14) (dual of [(4681, 14), 65494, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3240, 32767, F32, 14) (dual of [32767, 32727, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3240, 32767, F32, 14) (dual of [32767, 32727, 15]-code), using
(26, 40, 16385)-Net over F32 — Digital
Digital (26, 40, 16385)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3240, 16385, F32, 2, 14) (dual of [(16385, 2), 32730, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3240, 32770, F32, 14) (dual of [32770, 32730, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3240, 32771, F32, 14) (dual of [32771, 32731, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3240, 32771, F32, 14) (dual of [32771, 32731, 15]-code), using
- OOA 2-folding [i] based on linear OA(3240, 32770, F32, 14) (dual of [32770, 32730, 15]-code), using
(26, 40, large)-Net in Base 32 — Upper bound on s
There is no (26, 40, large)-net in base 32, because
- 12 times m-reduction [i] would yield (26, 28, large)-net in base 32, but