Best Known (24−8, 24, s)-Nets in Base 2
(24−8, 24, 39)-Net over F2 — Constructive and digital
Digital (16, 24, 39)-net over F2, using
- 23 times duplication [i] based on digital (13, 21, 39)-net over F2, using
(24−8, 24, 40)-Net over F2 — Digital
Digital (16, 24, 40)-net over F2, using
- 21 times duplication [i] based on digital (15, 23, 40)-net over F2, using
- net defined by OOA [i] based on linear OOA(223, 40, F2, 8, 8) (dual of [(40, 8), 297, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(223, 40, F2, 7, 8) (dual of [(40, 7), 257, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(223, 40, F2, 2, 8) (dual of [(40, 2), 57, 9]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(221, 39, F2, 2, 8) (dual of [(39, 2), 57, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (13, 21, 39)-net over F2, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(221, 39, F2, 2, 8) (dual of [(39, 2), 57, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(223, 40, F2, 2, 8) (dual of [(40, 2), 57, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(223, 40, F2, 7, 8) (dual of [(40, 7), 257, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(223, 40, F2, 8, 8) (dual of [(40, 8), 297, 9]-NRT-code), using
(24−8, 24, 136)-Net in Base 2 — Upper bound on s
There is no (16, 24, 137)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 17 138838 > 224 [i]