Best Known (126, 126+74, s)-Nets in Base 2
(126, 126+74, 69)-Net over F2 — Constructive and digital
Digital (126, 200, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 56, 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, 144, 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, 56, 20)-net over F2, using
(126, 126+74, 72)-Net in Base 2 — Constructive
(126, 200, 72)-net in base 2, using
- trace code for nets [i] based on (26, 100, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-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 3 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]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
(126, 126+74, 110)-Net over F2 — Digital
Digital (126, 200, 110)-net over F2, using
- trace code for nets [i] based on digital (26, 100, 55)-net over F4, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 26 and N(F) ≥ 55, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
(126, 126+74, 568)-Net in Base 2 — Upper bound on s
There is no (126, 200, 569)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 691739 376186 681362 615552 389274 634848 920870 188521 654677 572404 > 2200 [i]