Best Known (39−7, 39, s)-Nets in Base 32
(39−7, 39, 5592400)-Net over F32 — Constructive and digital
Digital (32, 39, 5592400)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 8, 3214400)-net over F32, using
- net defined by OOA [i] based on linear OOA(328, 3214400, F32, 3, 3) (dual of [(3214400, 3), 9643192, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(328, 3214400, F32, 2, 3) (dual of [(3214400, 2), 6428792, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(328, 3214400, F32, 3, 3) (dual of [(3214400, 3), 9643192, 4]-NRT-code), using
- digital (24, 31, 2796200)-net over F32, using
- net defined by OOA [i] based on linear OOA(3231, 2796200, F32, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3231, 8388601, F32, 7) (dual of [8388601, 8388570, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(3231, large, F32, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3231, large, F32, 7) (dual of [large, large−31, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3231, 8388601, F32, 7) (dual of [8388601, 8388570, 8]-code), using
- net defined by OOA [i] based on linear OOA(3231, 2796200, F32, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- digital (5, 8, 3214400)-net over F32, using
(39−7, 39, large)-Net over F32 — Digital
Digital (32, 39, large)-net over F32, using
- 2 times m-reduction [i] based on digital (32, 41, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
(39−7, 39, large)-Net in Base 32 — Upper bound on s
There is no (32, 39, large)-net in base 32, because
- 5 times m-reduction [i] would yield (32, 34, large)-net in base 32, but