Best Known (145, 231, s)-Nets in Base 2
(145, 231, 77)-Net over F2 — Constructive and digital
Digital (145, 231, 77)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (48, 91, 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, 140, 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, 91, 35)-net over F2, using
(145, 231, 84)-Net in Base 2 — Constructive
(145, 231, 84)-net in base 2, using
- 5 times m-reduction [i] based on (145, 236, 84)-net in base 2, using
- trace code for nets [i] based on (27, 118, 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, 118, 42)-net in base 4, using
(145, 231, 123)-Net over F2 — Digital
Digital (145, 231, 123)-net over F2, using
(145, 231, 637)-Net in Base 2 — Upper bound on s
There is no (145, 231, 638)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3493 770256 422529 887203 089822 056085 862785 655698 567789 155849 709555 478298 > 2231 [i]