Best Known (219−136, 219, s)-Nets in Base 2
(219−136, 219, 51)-Net over F2 — Constructive and digital
Digital (83, 219, 51)-net over F2, using
- t-expansion [i] based on digital (80, 219, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 2 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (80, 50)-sequence over F2, using
(219−136, 219, 57)-Net over F2 — Digital
Digital (83, 219, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
(219−136, 219, 158)-Net in Base 2 — Upper bound on s
There is no (83, 219, 159)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 069466 712751 956019 661581 994334 387109 628641 027960 850581 112331 011190 > 2219 [i]