Best Known (162−44, 162, s)-Nets in Base 2
(162−44, 162, 138)-Net over F2 — Constructive and digital
Digital (118, 162, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 54, 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
(162−44, 162, 191)-Net over F2 — Digital
Digital (118, 162, 191)-net over F2, using
(162−44, 162, 1458)-Net in Base 2 — Upper bound on s
There is no (118, 162, 1459)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 5 846551 290257 466742 800788 245291 920300 166874 804392 > 2162 [i]