Best Known (85, 85+9, s)-Nets in Base 2
(85, 85+9, 2097150)-Net over F2 — Constructive and digital
Digital (85, 94, 2097150)-net over F2, using
- 21 times duplication [i] based on digital (84, 93, 2097150)-net over F2, using
- net defined by OOA [i] based on linear OOA(293, 2097150, F2, 9, 9) (dual of [(2097150, 9), 18874257, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(293, 2097150, F2, 8, 9) (dual of [(2097150, 8), 16777107, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(293, 8388601, F2, 9) (dual of [8388601, 8388508, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(293, 8388601, F2, 9) (dual of [8388601, 8388508, 10]-code), using
- appending kth column [i] based on linear OOA(293, 2097150, F2, 8, 9) (dual of [(2097150, 8), 16777107, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(293, 2097150, F2, 9, 9) (dual of [(2097150, 9), 18874257, 10]-NRT-code), using
(85, 85+9, large)-Net in Base 2 — Upper bound on s
There is no (85, 94, large)-net in base 2, because
- 7 times m-reduction [i] would yield (85, 87, large)-net in base 2, but