Best Known (150−11, 150, s)-Nets in Base 2
(150−11, 150, 4194321)-Net over F2 — Constructive and digital
Digital (139, 150, 4194321)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (5, 10, 20)-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
(150−11, 150, 7088396)-Net over F2 — Digital
Digital (139, 150, 7088396)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2150, 7088396, F2, 3, 11) (dual of [(7088396, 3), 21265038, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2150, large, F2, 3, 11), using
- 21 times duplication [i] based on linear OOA(2149, large, F2, 3, 11), using
- 3 times NRT-code embedding in larger space [i] based on linear OOA(2140, large, F2, 3, 11), using
- 21 times duplication [i] based on linear OOA(2149, large, F2, 3, 11), using
- discarding factors / shortening the dual code based on linear OOA(2150, large, F2, 3, 11), using
(150−11, 150, large)-Net in Base 2 — Upper bound on s
There is no (139, 150, large)-net in base 2, because
- 9 times m-reduction [i] would yield (139, 141, large)-net in base 2, but