Best Known (88, 123, s)-Nets in Base 2
(88, 123, 84)-Net over F2 — Constructive and digital
Digital (88, 123, 84)-net over F2, using
- t-expansion [i] based on digital (87, 123, 84)-net over F2, using
- trace code for nets [i] based on digital (5, 41, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- trace code for nets [i] based on digital (5, 41, 28)-net over F8, using
(88, 123, 137)-Net over F2 — Digital
Digital (88, 123, 137)-net over F2, using
(88, 123, 1013)-Net in Base 2 — Upper bound on s
There is no (88, 123, 1014)-net in base 2, because
- 1 times m-reduction [i] would yield (88, 122, 1014)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 5 363879 249346 723898 459096 480043 164497 > 2122 [i]