Best Known (158, 158+64, s)-Nets in Base 2
(158, 158+64, 138)-Net over F2 — Constructive and digital
Digital (158, 222, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 74, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
(158, 158+64, 215)-Net over F2 — Digital
Digital (158, 222, 215)-net over F2, using
(158, 158+64, 1520)-Net in Base 2 — Upper bound on s
There is no (158, 222, 1521)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 754434 040845 972959 841949 354869 814890 478876 454294 418885 746432 696533 > 2222 [i]