Best Known (27−7, 27, s)-Nets in Base 2
(27−7, 27, 254)-Net over F2 — Constructive and digital
Digital (20, 27, 254)-net over F2, using
- 21 times duplication [i] based on digital (19, 26, 254)-net over F2, using
- net defined by OOA [i] based on linear OOA(226, 254, F2, 7, 7) (dual of [(254, 7), 1752, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(226, 255, F2, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(226, 254, F2, 7, 7) (dual of [(254, 7), 1752, 8]-NRT-code), using
(27−7, 27, 255)-Net over F2 — Digital
Digital (20, 27, 255)-net over F2, using
- 21 times duplication [i] based on digital (19, 26, 255)-net over F2, using
- net defined by OOA [i] based on linear OOA(226, 255, F2, 7, 7) (dual of [(255, 7), 1759, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(226, 255, F2, 6, 7) (dual of [(255, 6), 1504, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(226, 255, F2, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(226, 255, F2, 6, 7) (dual of [(255, 6), 1504, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(226, 255, F2, 7, 7) (dual of [(255, 7), 1759, 8]-NRT-code), using
(27−7, 27, 734)-Net in Base 2 — Upper bound on s
There is no (20, 27, 735)-net in base 2, because
- 1 times m-reduction [i] would yield (20, 26, 735)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 67 261566 > 226 [i]