Best Known (89, 89+15, s)-Nets in Base 32
(89, 89+15, 2396742)-Net over F32 — Constructive and digital
Digital (89, 104, 2396742)-net over F32, using
- 322 times duplication [i] based on digital (87, 102, 2396742)-net over F32, using
- (u, u+v)-construction [i] based on
- 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 (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
- digital (24, 31, 2796200)-net over F32, using
- (u, u+v)-construction [i] based on
(89, 89+15, large)-Net over F32 — Digital
Digital (89, 104, large)-net over F32, using
- t-expansion [i] based on digital (87, 104, large)-net over F32, using
- 6 times m-reduction [i] based on digital (87, 110, large)-net over F32, using
(89, 89+15, large)-Net in Base 32 — Upper bound on s
There is no (89, 104, large)-net in base 32, because
- 13 times m-reduction [i] would yield (89, 91, large)-net in base 32, but