Best Known (60, 60+15, s)-Nets in Base 32
(60, 60+15, 1198371)-Net over F32 — Constructive and digital
Digital (60, 75, 1198371)-net over F32, using
- 324 times duplication [i] based on digital (56, 71, 1198371)-net over F32, using
- net defined by OOA [i] based on linear OOA(3271, 1198371, F32, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3271, 8388598, F32, 15) (dual of [8388598, 8388527, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3271, large, F32, 15) (dual of [large, large−71, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3271, large, F32, 15) (dual of [large, large−71, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3271, 8388598, F32, 15) (dual of [8388598, 8388527, 16]-code), using
- net defined by OOA [i] based on linear OOA(3271, 1198371, F32, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
(60, 60+15, large)-Net over F32 — Digital
Digital (60, 75, large)-net over F32, using
- 1 times m-reduction [i] based on digital (60, 76, large)-net over F32, using
(60, 60+15, large)-Net in Base 32 — Upper bound on s
There is no (60, 75, large)-net in base 32, because
- 13 times m-reduction [i] would yield (60, 62, large)-net in base 32, but