Best Known (166, 166+67, s)-Nets in Base 2
(166, 166+67, 138)-Net over F2 — Constructive and digital
Digital (166, 233, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (166, 234, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 78, 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
- trace code for nets [i] based on digital (10, 78, 46)-net over F8, using
(166, 166+67, 225)-Net over F2 — Digital
Digital (166, 233, 225)-net over F2, using
(166, 166+67, 1672)-Net in Base 2 — Upper bound on s
There is no (166, 233, 1673)-net in base 2, because
- 1 times m-reduction [i] would yield (166, 232, 1673)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 7001 187569 864699 181729 884144 965905 012569 246437 205167 854085 667793 370584 > 2232 [i]