Best Known (128, 205, s)-Nets in Base 2
(128, 205, 69)-Net over F2 — Constructive and digital
Digital (128, 205, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 77, 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, 128, 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, 77, 33)-net over F2, using
(128, 205, 70)-Net in Base 2 — Constructive
(128, 205, 70)-net in base 2, using
- 3 times m-reduction [i] based on (128, 208, 70)-net in base 2, using
- trace code for nets [i] based on (24, 104, 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, 104, 35)-net in base 4, using
(128, 205, 109)-Net over F2 — Digital
Digital (128, 205, 109)-net over F2, using
(128, 205, 566)-Net in Base 2 — Upper bound on s
There is no (128, 205, 567)-net in base 2, because
- 1 times m-reduction [i] would yield (128, 204, 567)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 26 660895 522283 104083 094413 575945 889291 188867 056426 152427 704575 > 2204 [i]