Best Known (73−9, 73, s)-Nets in Base 2
(73−9, 73, 65536)-Net over F2 — Constructive and digital
Digital (64, 73, 65536)-net over F2, using
- net defined by OOA [i] based on linear OOA(273, 65536, F2, 9, 9) (dual of [(65536, 9), 589751, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(273, 65536, F2, 8, 9) (dual of [(65536, 8), 524215, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(273, 262145, F2, 9) (dual of [262145, 262072, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, 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(273, 262145, F2, 9) (dual of [262145, 262072, 10]-code), using
- appending kth column [i] based on linear OOA(273, 65536, F2, 8, 9) (dual of [(65536, 8), 524215, 10]-NRT-code), using
(73−9, 73, 580214)-Net in Base 2 — Upper bound on s
There is no (64, 73, 580215)-net in base 2, because
- 1 times m-reduction [i] would yield (64, 72, 580215)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 4722 381121 957753 140611 > 272 [i]