Best Known (16, 16+3, s)-Nets in Base 2
(16, 16+3, 262143)-Net over F2 — Constructive and digital
Digital (16, 19, 262143)-net over F2, using
- net defined by OOA [i] based on linear OOA(219, 262143, F2, 3, 3) (dual of [(262143, 3), 786410, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(219, 262144, F2, 3) (dual of [262144, 262125, 4]-code or 262144-cap in PG(18,2)), using
- Reed–Muller code RM(1,18) [i]
- caps in base b = 2 [i]
- OOA stacking with additional row [i] based on linear OA(219, 262144, F2, 3) (dual of [262144, 262125, 4]-code or 262144-cap in PG(18,2)), using
(16, 16+3, 262143)-Net in Base 2 — Upper bound on s
There is no (16, 19, 262144)-net in base 2, because
- 1 times m-reduction [i] would yield (16, 18, 262144)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 262145 > 218 [i]