Best Known (140, 140+11, s)-Nets in Base 2
(140, 140+11, 4194327)-Net over F2 — Constructive and digital
Digital (140, 151, 4194327)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (6, 11, 26)-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
(140, 140+11, 7826225)-Net over F2 — Digital
Digital (140, 151, 7826225)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2151, 7826225, F2, 3, 11) (dual of [(7826225, 3), 23478524, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2151, large, F2, 3, 11), using
- 22 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
- 22 times duplication [i] based on linear OOA(2149, large, F2, 3, 11), using
- discarding factors / shortening the dual code based on linear OOA(2151, large, F2, 3, 11), using
(140, 140+11, large)-Net in Base 2 — Upper bound on s
There is no (140, 151, large)-net in base 2, because
- 9 times m-reduction [i] would yield (140, 142, large)-net in base 2, but