Best Known (165, 165+11, s)-Nets in Base 2
(165, 165+11, 4325374)-Net over F2 — Constructive and digital
Digital (165, 176, 4325374)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (31, 36, 131073)-net over F2, using
- digital (129, 140, 4194301)-net over F2, using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2140, large, F2, 3, 11), using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
(165, 165+11, large)-Net over F2 — Digital
Digital (165, 176, large)-net over F2, using
- 224 times duplication [i] based on digital (141, 152, large)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
- 4 times NRT-code embedding in larger space [i] based on linear OOA(2140, large, F2, 3, 11), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
(165, 165+11, large)-Net in Base 2 — Upper bound on s
There is no (165, 176, large)-net in base 2, because
- 9 times m-reduction [i] would yield (165, 167, large)-net in base 2, but