Best Known (21, 27, s)-Nets in Base 2
(21, 27, 254)-Net over F2 — Constructive and digital
Digital (21, 27, 254)-net over F2, using
- 21 times duplication [i] based on digital (20, 26, 254)-net over F2, using
- net defined by OOA [i] based on linear OOA(226, 254, F2, 6, 6) (dual of [(254, 6), 1498, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(226, 255, F2, 3, 6) (dual of [(255, 3), 739, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(226, 255, F2, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(226, 255, F2, 3, 6) (dual of [(255, 3), 739, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(226, 254, F2, 6, 6) (dual of [(254, 6), 1498, 7]-NRT-code), using
(21, 27, 256)-Net over F2 — Digital
Digital (21, 27, 256)-net over F2, using
- net defined by OOA [i] based on linear OOA(227, 256, F2, 6, 6) (dual of [(256, 6), 1509, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(227, 256, F2, 5, 6) (dual of [(256, 5), 1253, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(227, 256, F2, 2, 6) (dual of [(256, 2), 485, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(225, 255, F2, 2, 6) (dual of [(255, 2), 485, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(227, 256, F2, 2, 6) (dual of [(256, 2), 485, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(227, 256, F2, 5, 6) (dual of [(256, 5), 1253, 7]-NRT-code), using
(21, 27, 926)-Net in Base 2 — Upper bound on s
There is no (21, 27, 927)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 134 489470 > 227 [i]