Best Known (58−20, 58, s)-Nets in Base 32
(58−20, 58, 3277)-Net over F32 — Constructive and digital
Digital (38, 58, 3277)-net over F32, using
- net defined by OOA [i] based on linear OOA(3258, 3277, F32, 20, 20) (dual of [(3277, 20), 65482, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3258, 32770, F32, 20) (dual of [32770, 32712, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3258, 32771, F32, 20) (dual of [32771, 32713, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3255, 32768, F32, 19) (dual of [32768, 32713, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3258, 32771, F32, 20) (dual of [32771, 32713, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3258, 32770, F32, 20) (dual of [32770, 32712, 21]-code), using
(58−20, 58, 16385)-Net over F32 — Digital
Digital (38, 58, 16385)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3258, 16385, F32, 2, 20) (dual of [(16385, 2), 32712, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3258, 32770, F32, 20) (dual of [32770, 32712, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3258, 32771, F32, 20) (dual of [32771, 32713, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3255, 32768, F32, 19) (dual of [32768, 32713, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3258, 32771, F32, 20) (dual of [32771, 32713, 21]-code), using
- OOA 2-folding [i] based on linear OA(3258, 32770, F32, 20) (dual of [32770, 32712, 21]-code), using
(58−20, 58, large)-Net in Base 32 — Upper bound on s
There is no (38, 58, large)-net in base 32, because
- 18 times m-reduction [i] would yield (38, 40, large)-net in base 32, but