Best Known (81, 81+126, s)-Nets in Base 2
(81, 81+126, 51)-Net over F2 — Constructive and digital
Digital (81, 207, 51)-net over F2, using
- t-expansion [i] based on digital (80, 207, 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
(81, 81+126, 56)-Net over F2 — Digital
Digital (81, 207, 56)-net over F2, using
- t-expansion [i] based on digital (80, 207, 56)-net over F2, using
- net from sequence [i] based on digital (80, 55)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 80 and N(F) ≥ 56, using
- net from sequence [i] based on digital (80, 55)-sequence over F2, using
(81, 81+126, 157)-Net in Base 2 — Upper bound on s
There is no (81, 207, 158)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 262 369162 712782 883706 814084 100329 948760 790384 403873 539456 687472 > 2207 [i]