Best Known (109−26, 109, s)-Nets in Base 2
(109−26, 109, 138)-Net over F2 — Constructive and digital
Digital (83, 109, 138)-net over F2, using
- 21 times duplication [i] based on digital (82, 108, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 36, 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, 36, 46)-net over F8, using
(109−26, 109, 195)-Net over F2 — Digital
Digital (83, 109, 195)-net over F2, using
(109−26, 109, 1875)-Net in Base 2 — Upper bound on s
There is no (83, 109, 1876)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 652 205705 608215 719833 911702 898692 > 2109 [i]