Best Known (127, 138, s)-Nets in Base 2
(127, 138, 2097151)-Net over F2 — Constructive and digital
Digital (127, 138, 2097151)-net over F2, using
- 24 times duplication [i] based on digital (123, 134, 2097151)-net over F2, using
- net defined by OOA [i] based on linear OOA(2134, 2097151, F2, 15, 11) (dual of [(2097151, 15), 31457131, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2134, 4194303, F2, 3, 11) (dual of [(4194303, 3), 12582775, 12]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2134, 2097151, F2, 15, 11) (dual of [(2097151, 15), 31457131, 12]-NRT-code), using
(127, 138, 2160206)-Net over F2 — Digital
Digital (127, 138, 2160206)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2138, 2160206, F2, 3, 11) (dual of [(2160206, 3), 6480480, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2138, 4194304, F2, 3, 11) (dual of [(4194304, 3), 12582774, 12]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2137, 4194304, F2, 3, 11) (dual of [(4194304, 3), 12582775, 12]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2134, 4194303, F2, 3, 11) (dual of [(4194303, 3), 12582775, 12]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2137, 4194304, F2, 3, 11) (dual of [(4194304, 3), 12582775, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2138, 4194304, F2, 3, 11) (dual of [(4194304, 3), 12582774, 12]-NRT-code), using
(127, 138, large)-Net in Base 2 — Upper bound on s
There is no (127, 138, large)-net in base 2, because
- 9 times m-reduction [i] would yield (127, 129, large)-net in base 2, but