Best Known (85−9, 85, s)-Nets in Base 2
(85−9, 85, 524288)-Net over F2 — Constructive and digital
Digital (76, 85, 524288)-net over F2, using
- net defined by OOA [i] based on linear OOA(285, 524288, F2, 9, 9) (dual of [(524288, 9), 4718507, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(285, 524288, F2, 8, 9) (dual of [(524288, 8), 4194219, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(285, 2097153, F2, 9) (dual of [2097153, 2097068, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(285, 2097153, F2, 9) (dual of [2097153, 2097068, 10]-code), using
- appending kth column [i] based on linear OOA(285, 524288, F2, 8, 9) (dual of [(524288, 8), 4194219, 10]-NRT-code), using
(85−9, 85, 4641754)-Net in Base 2 — Upper bound on s
There is no (76, 85, 4641755)-net in base 2, because
- 1 times m-reduction [i] would yield (76, 84, 4641755)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 19 342814 738523 307963 660446 > 284 [i]