Best Known (19, 22, s)-Nets in Base 2
(19, 22, 2097151)-Net over F2 — Constructive and digital
Digital (19, 22, 2097151)-net over F2, using
- net defined by OOA [i] based on linear OOA(222, 2097151, F2, 3, 3) (dual of [(2097151, 3), 6291431, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(222, 2097152, F2, 3) (dual of [2097152, 2097130, 4]-code or 2097152-cap in PG(21,2)), using
- Reed–Muller code RM(1,21) [i]
- caps in base b = 2 [i]
- OOA stacking with additional row [i] based on linear OA(222, 2097152, F2, 3) (dual of [2097152, 2097130, 4]-code or 2097152-cap in PG(21,2)), using
(19, 22, 2097151)-Net in Base 2 — Upper bound on s
There is no (19, 22, 2097152)-net in base 2, because
- 1 times m-reduction [i] would yield (19, 21, 2097152)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 2 097153 > 221 [i]