Best Known (14, 17, s)-Nets in Base 2
(14, 17, 65535)-Net over F2 — Constructive and digital
Digital (14, 17, 65535)-net over F2, using
- net defined by OOA [i] based on linear OOA(217, 65535, F2, 3, 3) (dual of [(65535, 3), 196588, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(217, 65536, F2, 3) (dual of [65536, 65519, 4]-code or 65536-cap in PG(16,2)), using
- Reed–Muller code RM(1,16) [i]
- caps in base b = 2 [i]
- OOA stacking with additional row [i] based on linear OA(217, 65536, F2, 3) (dual of [65536, 65519, 4]-code or 65536-cap in PG(16,2)), using
(14, 17, 65535)-Net in Base 2 — Upper bound on s
There is no (14, 17, 65536)-net in base 2, because
- 1 times m-reduction [i] would yield (14, 16, 65536)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 65537 > 216 [i]