Best Known (25, 25+6, s)-Nets in Base 2
(25, 25+6, 1022)-Net over F2 — Constructive and digital
Digital (25, 31, 1022)-net over F2, using
- 1 times m-reduction [i] based on digital (25, 32, 1022)-net over F2, using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(232, 1023, F2, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
(25, 25+6, 1023)-Net over F2 — Digital
Digital (25, 31, 1023)-net over F2, using
- net defined by OOA [i] based on linear OOA(231, 1023, F2, 6, 6) (dual of [(1023, 6), 6107, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(231, 1023, F2, 5, 6) (dual of [(1023, 5), 5084, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(231, 1023, F2, 2, 6) (dual of [(1023, 2), 2015, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(231, 1023, F2, 5, 6) (dual of [(1023, 5), 5084, 7]-NRT-code), using
(25, 25+6, 2340)-Net in Base 2 — Upper bound on s
There is no (25, 31, 2341)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2149 194848 > 231 [i]