Best Known (147, 235, s)-Nets in Base 2
(147, 235, 77)-Net over F2 — Constructive and digital
Digital (147, 235, 77)-net over F2, using
- 2 times m-reduction [i] based on digital (147, 237, 77)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (48, 93, 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 (54, 144, 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 (48, 93, 35)-net over F2, using
- (u, u+v)-construction [i] based on
(147, 235, 84)-Net in Base 2 — Constructive
(147, 235, 84)-net in base 2, using
- 5 times m-reduction [i] based on (147, 240, 84)-net in base 2, using
- trace code for nets [i] based on (27, 120, 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, 120, 42)-net in base 4, using
(147, 235, 123)-Net over F2 — Digital
Digital (147, 235, 123)-net over F2, using
(147, 235, 636)-Net in Base 2 — Upper bound on s
There is no (147, 235, 637)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 56893 045480 951100 944010 795978 503052 273708 602955 480802 822887 104645 685283 > 2235 [i]