Best Known (26, 33, s)-Nets in Base 2
(26, 33, 1022)-Net over F2 — Constructive and digital
Digital (26, 33, 1022)-net over F2, using
- 21 times duplication [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
(26, 33, 1023)-Net over F2 — Digital
Digital (26, 33, 1023)-net over F2, using
- 21 times duplication [i] based on digital (25, 32, 1023)-net over F2, using
- net defined by OOA [i] based on linear OOA(232, 1023, F2, 7, 7) (dual of [(1023, 7), 7129, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(232, 1023, F2, 6, 7) (dual of [(1023, 6), 6106, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(232, 1023, F2, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(232, 1023, F2, 6, 7) (dual of [(1023, 6), 6106, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(232, 1023, F2, 7, 7) (dual of [(1023, 7), 7129, 8]-NRT-code), using
(26, 33, 2949)-Net in Base 2 — Upper bound on s
There is no (26, 33, 2950)-net in base 2, because
- 1 times m-reduction [i] would yield (26, 32, 2950)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 4296 148426 > 232 [i]