Best Known (8, 11, s)-Nets in Base 2
(8, 11, 1023)-Net over F2 — Constructive and digital
Digital (8, 11, 1023)-net over F2, using
- net defined by OOA [i] based on linear OOA(211, 1023, F2, 3, 3) (dual of [(1023, 3), 3058, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(211, 1024, F2, 3) (dual of [1024, 1013, 4]-code or 1024-cap in PG(10,2)), using
- Reed–Muller code RM(1,10) [i]
- caps in base b = 2 [i]
- OOA stacking with additional row [i] based on linear OA(211, 1024, F2, 3) (dual of [1024, 1013, 4]-code or 1024-cap in PG(10,2)), using
(8, 11, 1023)-Net in Base 2 — Upper bound on s
There is no (8, 11, 1024)-net in base 2, because
- 1 times m-reduction [i] would yield (8, 10, 1024)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 1025 > 210 [i]