Best Known (139, 139+80, s)-Nets in Base 2
(139, 139+80, 76)-Net over F2 — Constructive and digital
Digital (139, 219, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (45, 85, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-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 1 place 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 (45, 33)-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 (45, 85, 34)-net over F2, using
(139, 139+80, 84)-Net in Base 2 — Constructive
(139, 219, 84)-net in base 2, using
- 5 times m-reduction [i] based on (139, 224, 84)-net in base 2, using
- trace code for nets [i] based on (27, 112, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [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
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- trace code for nets [i] based on (27, 112, 42)-net in base 4, using
(139, 139+80, 122)-Net over F2 — Digital
Digital (139, 219, 122)-net over F2, using
(139, 139+80, 644)-Net in Base 2 — Upper bound on s
There is no (139, 219, 645)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 889461 679766 677081 011133 635248 059300 463178 841506 969656 172466 167696 > 2219 [i]