Best Known (24, 24+13, s)-Nets in Base 32
(24, 24+13, 5461)-Net over F32 — Constructive and digital
Digital (24, 37, 5461)-net over F32, using
- net defined by OOA [i] based on linear OOA(3237, 5461, F32, 13, 13) (dual of [(5461, 13), 70956, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3237, 32767, F32, 13) (dual of [32767, 32730, 14]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3237, 32767, F32, 13) (dual of [32767, 32730, 14]-code), using
(24, 24+13, 16385)-Net over F32 — Digital
Digital (24, 37, 16385)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3237, 16385, F32, 2, 13) (dual of [(16385, 2), 32733, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3237, 32770, F32, 13) (dual of [32770, 32733, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3237, 32771, F32, 13) (dual of [32771, 32734, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- 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(3234, 32768, F32, 12) (dual of [32768, 32734, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(3237, 32771, F32, 13) (dual of [32771, 32734, 14]-code), using
- OOA 2-folding [i] based on linear OA(3237, 32770, F32, 13) (dual of [32770, 32733, 14]-code), using
(24, 24+13, large)-Net in Base 32 — Upper bound on s
There is no (24, 37, large)-net in base 32, because
- 11 times m-reduction [i] would yield (24, 26, large)-net in base 32, but