Best Known (28, 28+15, s)-Nets in Base 32
(28, 28+15, 4681)-Net over F32 — Constructive and digital
Digital (28, 43, 4681)-net over F32, using
- net defined by OOA [i] based on linear OOA(3243, 4681, F32, 15, 15) (dual of [(4681, 15), 70172, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3243, 32768, F32, 15) (dual of [32768, 32725, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(3243, 32768, F32, 15) (dual of [32768, 32725, 16]-code), using
(28, 28+15, 16385)-Net over F32 — Digital
Digital (28, 43, 16385)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3243, 16385, F32, 2, 15) (dual of [(16385, 2), 32727, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3243, 32770, F32, 15) (dual of [32770, 32727, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3243, 32771, F32, 15) (dual of [32771, 32728, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(3243, 32768, F32, 15) (dual of [32768, 32725, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(14) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3243, 32771, F32, 15) (dual of [32771, 32728, 16]-code), using
- OOA 2-folding [i] based on linear OA(3243, 32770, F32, 15) (dual of [32770, 32727, 16]-code), using
(28, 28+15, large)-Net in Base 32 — Upper bound on s
There is no (28, 43, large)-net in base 32, because
- 13 times m-reduction [i] would yield (28, 30, large)-net in base 32, but