Best Known (90, 90+128, s)-Nets in Base 2
(90, 90+128, 53)-Net over F2 — Constructive and digital
Digital (90, 218, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-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 4 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]
(90, 90+128, 57)-Net over F2 — Digital
Digital (90, 218, 57)-net over F2, using
- t-expansion [i] based on digital (83, 218, 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
(90, 90+128, 179)-Net in Base 2 — Upper bound on s
There is no (90, 218, 180)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 482912 439781 880022 369495 652334 633885 215360 242733 843005 460832 606682 > 2218 [i]