Best Known (123, 123+10, s)-Nets in Base 2
(123, 123+10, 2097151)-Net over F2 — Constructive and digital
Digital (123, 133, 2097151)-net over F2, using
- 1 times m-reduction [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
(123, 123+10, 4194302)-Net over F2 — Digital
Digital (123, 133, 4194302)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2133, 4194302, F2, 3, 10) (dual of [(4194302, 3), 12582773, 11]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2134, 4194303, F2, 3, 11) (dual of [(4194303, 3), 12582775, 12]-NRT-code), using
(123, 123+10, large)-Net in Base 2 — Upper bound on s
There is no (123, 133, large)-net in base 2, because
- 8 times m-reduction [i] would yield (123, 125, large)-net in base 2, but