Best Known (58, 88, s)-Nets in Base 32
(58, 88, 2184)-Net over F32 — Constructive and digital
Digital (58, 88, 2184)-net over F32, using
- net defined by OOA [i] based on linear OOA(3288, 2184, F32, 30, 30) (dual of [(2184, 30), 65432, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3288, 32760, F32, 30) (dual of [32760, 32672, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3288, 32760, F32, 30) (dual of [32760, 32672, 31]-code), using
(58, 88, 17299)-Net over F32 — Digital
Digital (58, 88, 17299)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3288, 17299, F32, 30) (dual of [17299, 17211, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using
(58, 88, large)-Net in Base 32 — Upper bound on s
There is no (58, 88, large)-net in base 32, because
- 28 times m-reduction [i] would yield (58, 60, large)-net in base 32, but