Best Known (17, 17+3, s)-Nets in Base 2
(17, 17+3, 524287)-Net over F2 — Constructive and digital
Digital (17, 20, 524287)-net over F2, using
- net defined by OOA [i] based on linear OOA(220, 524287, F2, 3, 3) (dual of [(524287, 3), 1572841, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(220, 524288, F2, 3) (dual of [524288, 524268, 4]-code or 524288-cap in PG(19,2)), using
- Reed–Muller code RM(1,19) [i]
- caps in base b = 2 [i]
- OOA stacking with additional row [i] based on linear OA(220, 524288, F2, 3) (dual of [524288, 524268, 4]-code or 524288-cap in PG(19,2)), using
(17, 17+3, 524287)-Net in Base 2 — Upper bound on s
There is no (17, 20, 524288)-net in base 2, because
- 1 times m-reduction [i] would yield (17, 19, 524288)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 524289 > 219 [i]