Best Known (129, 129+78, s)-Nets in Base 2
(129, 129+78, 69)-Net over F2 — Constructive and digital
Digital (129, 207, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 78, 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 (51, 129, 36)-net over F2, using
- net from sequence [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]
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
- digital (39, 78, 33)-net over F2, using
(129, 129+78, 70)-Net in Base 2 — Constructive
(129, 207, 70)-net in base 2, using
- 3 times m-reduction [i] based on (129, 210, 70)-net in base 2, using
- trace code for nets [i] based on (24, 105, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [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]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- trace code for nets [i] based on (24, 105, 35)-net in base 4, using
(129, 129+78, 109)-Net over F2 — Digital
Digital (129, 207, 109)-net over F2, using
(129, 129+78, 554)-Net in Base 2 — Upper bound on s
There is no (129, 207, 555)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 216 284273 417800 824677 345860 142723 116969 668182 101889 772925 788996 > 2207 [i]