Best Known (159−43, 159, s)-Nets in Base 2
(159−43, 159, 138)-Net over F2 — Constructive and digital
Digital (116, 159, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 53, 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
(159−43, 159, 190)-Net over F2 — Digital
Digital (116, 159, 190)-net over F2, using
(159−43, 159, 1566)-Net in Base 2 — Upper bound on s
There is no (116, 159, 1567)-net in base 2, because
- 1 times m-reduction [i] would yield (116, 158, 1567)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 367468 376431 328547 990083 508842 496295 249580 458436 > 2158 [i]