Best Known (142, 254, s)-Nets in Base 2
(142, 254, 67)-Net over F2 — Constructive and digital
Digital (142, 254, 67)-net over F2, using
- 4 times m-reduction [i] based on digital (142, 258, 67)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 97, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- digital (45, 161, 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 (39, 97, 33)-net over F2, using
- (u, u+v)-construction [i] based on
(142, 254, 91)-Net over F2 — Digital
Digital (142, 254, 91)-net over F2, using
(142, 254, 425)-Net in Base 2 — Upper bound on s
There is no (142, 254, 426)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 29455 060205 062877 139942 514255 866616 023229 557502 657860 292693 261285 869429 453832 > 2254 [i]