Best Known (15, 15+3, s)-Nets in Base 2
(15, 15+3, 131071)-Net over F2 — Constructive and digital
Digital (15, 18, 131071)-net over F2, using
- net defined by OOA [i] based on linear OOA(218, 131071, F2, 3, 3) (dual of [(131071, 3), 393195, 4]-NRT-code), using
- OOA stacking with additional row [i] based on linear OA(218, 131072, F2, 3) (dual of [131072, 131054, 4]-code or 131072-cap in PG(17,2)), using
- Reed–Muller code RM(1,17) [i]
- caps in base b = 2 [i]
- OOA stacking with additional row [i] based on linear OA(218, 131072, F2, 3) (dual of [131072, 131054, 4]-code or 131072-cap in PG(17,2)), using
(15, 15+3, 131071)-Net in Base 2 — Upper bound on s
There is no (15, 18, 131072)-net in base 2, because
- 1 times m-reduction [i] would yield (15, 17, 131072)-net in base 2, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 2m ≥ 131073 > 217 [i]