Best Known (239−152, 239, s)-Nets in Base 2
(239−152, 239, 52)-Net over F2 — Constructive and digital
Digital (87, 239, 52)-net over F2, using
- t-expansion [i] based on digital (85, 239, 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]
- net from sequence [i] based on digital (85, 51)-sequence over F2, using
(239−152, 239, 57)-Net over F2 — Digital
Digital (87, 239, 57)-net over F2, using
- t-expansion [i] based on digital (83, 239, 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
(239−152, 239, 162)-Net in Base 2 — Upper bound on s
There is no (87, 239, 163)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 990654 957195 531206 763453 062592 574281 940732 322537 563624 726685 620810 689040 > 2239 [i]