Best Known (48, 48+17, s)-Nets in Base 32
(48, 48+17, 131072)-Net over F32 — Constructive and digital
Digital (48, 65, 131072)-net over F32, using
- net defined by OOA [i] based on linear OOA(3265, 131072, F32, 17, 17) (dual of [(131072, 17), 2228159, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3265, 1048577, F32, 17) (dual of [1048577, 1048512, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(3265, 1048577, F32, 17) (dual of [1048577, 1048512, 18]-code), using
(48, 48+17, 547486)-Net over F32 — Digital
Digital (48, 65, 547486)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3265, 547486, F32, 17) (dual of [547486, 547421, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3265, 1048576, F32, 17) (dual of [1048576, 1048511, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3265, 1048576, F32, 17) (dual of [1048576, 1048511, 18]-code), using
(48, 48+17, large)-Net in Base 32 — Upper bound on s
There is no (48, 65, large)-net in base 32, because
- 15 times m-reduction [i] would yield (48, 50, large)-net in base 32, but