Best Known (137, 137+11, s)-Nets in Base 2
(137, 137+11, 4194311)-Net over F2 — Constructive and digital
Digital (137, 148, 4194311)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (3, 8, 10)-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
(137, 137+11, 5814860)-Net over F2 — Digital
Digital (137, 148, 5814860)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2148, 5814860, F2, 3, 11) (dual of [(5814860, 3), 17444432, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2148, large, F2, 3, 11), using
- 22 times duplication [i] based on linear OOA(2146, large, F2, 3, 11), using
- 2 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(2146, large, F2, 3, 11), using
- discarding factors / shortening the dual code based on linear OOA(2148, large, F2, 3, 11), using
(137, 137+11, large)-Net in Base 2 — Upper bound on s
There is no (137, 148, large)-net in base 2, because
- 9 times m-reduction [i] would yield (137, 139, large)-net in base 2, but