Best Known (13−3, 13, s)-Nets in Base 2
(13−3, 13, 4095)-Net over F2 — Constructive and digital
Digital (10, 13, 4095)-net over F2, using
- net defined by OOA [i] based on linear OOA(213, 4095, F2, 3, 3) (dual of [(4095, 3), 12272, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(213, 4096, F2, 3) (dual of [4096, 4083, 4]-code or 4096-cap in PG(12,2)), using
- Reed–Muller code RM(1,12) [i]
- caps in base b = 2 [i]
- OOA stacking with additional row [i] based on linear OA(213, 4096, F2, 3) (dual of [4096, 4083, 4]-code or 4096-cap in PG(12,2)), using
(13−3, 13, 4095)-Net in Base 2 — Upper bound on s
There is no (10, 13, 4096)-net in base 2, because
- 1 times m-reduction [i] would yield (10, 12, 4096)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 4097 > 212 [i]