Best Known (23−6, 23, s)-Nets in Base 2
(23−6, 23, 127)-Net over F2 — Constructive and digital
Digital (17, 23, 127)-net over F2, using
- t-expansion [i] based on digital (16, 23, 127)-net over F2, using
(23−6, 23, 128)-Net over F2 — Digital
Digital (17, 23, 128)-net over F2, using
- net defined by OOA [i] based on linear OOA(223, 128, F2, 6, 6) (dual of [(128, 6), 745, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(223, 128, F2, 5, 6) (dual of [(128, 5), 617, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(223, 128, F2, 2, 6) (dual of [(128, 2), 233, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(221, 127, F2, 2, 6) (dual of [(127, 2), 233, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 21, 127)-net over F2, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(221, 127, F2, 2, 6) (dual of [(127, 2), 233, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(223, 128, F2, 2, 6) (dual of [(128, 2), 233, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(223, 128, F2, 5, 6) (dual of [(128, 5), 617, 7]-NRT-code), using
(23−6, 23, 365)-Net in Base 2 — Upper bound on s
There is no (17, 23, 366)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 8 440998 > 223 [i]