Best Known (9, 9+3, s)-Nets in Base 2
(9, 9+3, 2047)-Net over F2 — Constructive and digital
Digital (9, 12, 2047)-net over F2, using
- net defined by OOA [i] based on linear OOA(212, 2047, F2, 3, 3) (dual of [(2047, 3), 6129, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(212, 2048, F2, 3) (dual of [2048, 2036, 4]-code or 2048-cap in PG(11,2)), using
- Reed–Muller code RM(1,11) [i]
- caps in base b = 2 [i]
- OOA stacking with additional row [i] based on linear OA(212, 2048, F2, 3) (dual of [2048, 2036, 4]-code or 2048-cap in PG(11,2)), using
(9, 9+3, 2047)-Net in Base 2 — Upper bound on s
There is no (9, 12, 2048)-net in base 2, because
- 1 times m-reduction [i] would yield (9, 11, 2048)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 2049 > 211 [i]