Best Known (120, 182, s)-Nets in Base 2
(120, 182, 69)-Net over F2 — Constructive and digital
Digital (120, 182, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (41, 72, 34)-net over F2, using
- trace code for nets [i] based on digital (5, 36, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- trace code for nets [i] based on digital (5, 36, 17)-net over F4, using
- digital (48, 110, 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 (41, 72, 34)-net over F2, using
(120, 182, 84)-Net in Base 2 — Constructive
(120, 182, 84)-net in base 2, using
- 4 times m-reduction [i] based on (120, 186, 84)-net in base 2, using
- trace code for nets [i] based on (27, 93, 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, 93, 42)-net in base 4, using
(120, 182, 123)-Net over F2 — Digital
Digital (120, 182, 123)-net over F2, using
(120, 182, 682)-Net in Base 2 — Upper bound on s
There is no (120, 182, 683)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 394089 557014 032274 905523 482087 924455 579680 894769 026608 > 2182 [i]