Best Known (89−9, 89, s)-Nets in Base 2
(89−9, 89, 1048576)-Net over F2 — Constructive and digital
Digital (80, 89, 1048576)-net over F2, using
- net defined by OOA [i] based on linear OOA(289, 1048576, F2, 9, 9) (dual of [(1048576, 9), 9437095, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(289, 1048576, F2, 8, 9) (dual of [(1048576, 8), 8388519, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(289, 4194305, F2, 9) (dual of [4194305, 4194216, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4194305 | 244−1, 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(289, 4194305, F2, 9) (dual of [4194305, 4194216, 10]-code), using
- appending kth column [i] based on linear OOA(289, 1048576, F2, 8, 9) (dual of [(1048576, 8), 8388519, 10]-NRT-code), using
(89−9, 89, large)-Net in Base 2 — Upper bound on s
There is no (80, 89, large)-net in base 2, because
- 7 times m-reduction [i] would yield (80, 82, large)-net in base 2, but