Best Known (222−80, 222, s)-Nets in Base 2
(222−80, 222, 77)-Net over F2 — Constructive and digital
Digital (142, 222, 77)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (48, 88, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- digital (54, 134, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (48, 88, 35)-net over F2, using
(222−80, 222, 86)-Net in Base 2 — Constructive
(142, 222, 86)-net in base 2, using
- 2 times m-reduction [i] based on (142, 224, 86)-net in base 2, using
- trace code for nets [i] based on (30, 112, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- trace code for nets [i] based on (30, 112, 43)-net in base 4, using
(222−80, 222, 128)-Net over F2 — Digital
Digital (142, 222, 128)-net over F2, using
(222−80, 222, 681)-Net in Base 2 — Upper bound on s
There is no (142, 222, 682)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 974950 004764 228794 514547 962821 270135 431649 562453 361145 647690 656725 > 2222 [i]