Best Known (25−6, 25, s)-Nets in Base 2
(25−6, 25, 254)-Net over F2 — Constructive and digital
Digital (19, 25, 254)-net over F2, using
- 1 times m-reduction [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
(25−6, 25, 255)-Net over F2 — Digital
Digital (19, 25, 255)-net over F2, using
- net defined by OOA [i] based on linear OOA(225, 255, F2, 6, 6) (dual of [(255, 6), 1505, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(225, 255, F2, 5, 6) (dual of [(255, 5), 1250, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(225, 255, F2, 2, 6) (dual of [(255, 2), 485, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(225, 255, F2, 5, 6) (dual of [(255, 5), 1250, 7]-NRT-code), using
(25−6, 25, 582)-Net in Base 2 — Upper bound on s
There is no (19, 25, 583)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 33 708478 > 225 [i]