Best Known (166, 166+68, s)-Nets in Base 2
(166, 166+68, 138)-Net over F2 — Constructive and digital
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
(166, 166+68, 220)-Net over F2 — Digital
Digital (166, 234, 220)-net over F2, using
(166, 166+68, 1547)-Net in Base 2 — Upper bound on s
There is no (166, 234, 1548)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 28146 513602 603486 159552 624348 773108 824308 319807 437310 697730 037281 196272 > 2234 [i]