Best Known (187−64, 187, s)-Nets in Base 2
(187−64, 187, 70)-Net over F2 — Constructive and digital
Digital (123, 187, 70)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 53, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- digital (70, 134, 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 (21, 53, 21)-net over F2, using
(187−64, 187, 84)-Net in Base 2 — Constructive
(123, 187, 84)-net in base 2, using
- 5 times m-reduction [i] based on (123, 192, 84)-net in base 2, using
- trace code for nets [i] based on (27, 96, 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, 96, 42)-net in base 4, using
(187−64, 187, 124)-Net over F2 — Digital
Digital (123, 187, 124)-net over F2, using
(187−64, 187, 688)-Net in Base 2 — Upper bound on s
There is no (123, 187, 689)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 201 257533 370410 670086 959828 395189 095003 970487 541641 353859 > 2187 [i]