Best Known (223−138, 223, s)-Nets in Base 2
(223−138, 223, 52)-Net over F2 — Constructive and digital
Digital (85, 223, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-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 3 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]
(223−138, 223, 57)-Net over F2 — Digital
Digital (85, 223, 57)-net over F2, using
- t-expansion [i] based on digital (83, 223, 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
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(223−138, 223, 162)-Net in Base 2 — Upper bound on s
There is no (85, 223, 163)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 16 913867 323754 179492 098841 797484 359535 082194 003814 293708 978839 066656 > 2223 [i]