Best Known (224−141, 224, s)-Nets in Base 2
(224−141, 224, 51)-Net over F2 — Constructive and digital
Digital (83, 224, 51)-net over F2, using
- t-expansion [i] based on digital (80, 224, 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
(224−141, 224, 57)-Net over F2 — Digital
Digital (83, 224, 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
(224−141, 224, 156)-Net in Base 2 — Upper bound on s
There is no (83, 224, 157)-net in base 2, because
- 1 times m-reduction [i] would yield (83, 223, 157)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 13 794504 177736 596189 023874 689309 898280 266391 431391 423527 146744 735824 > 2223 [i]