Best Known (122, 122+66, s)-Nets in Base 2
(122, 122+66, 69)-Net over F2 — Constructive and digital
Digital (122, 188, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 52, 20)-net over F2, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- digital (70, 136, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [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 (70, 48)-sequence over F2, using
- digital (19, 52, 20)-net over F2, using
(122, 122+66, 84)-Net in Base 2 — Constructive
(122, 188, 84)-net in base 2, using
- 2 times m-reduction [i] based on (122, 190, 84)-net in base 2, using
- trace code for nets [i] based on (27, 95, 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, 95, 42)-net in base 4, using
(122, 122+66, 118)-Net over F2 — Digital
Digital (122, 188, 118)-net over F2, using
(122, 122+66, 635)-Net in Base 2 — Upper bound on s
There is no (122, 188, 636)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 404 315298 872187 350280 189058 054985 516876 478808 834784 762729 > 2188 [i]