Best Known (135, 135+75, s)-Nets in Base 2
(135, 135+75, 76)-Net over F2 — Constructive and digital
Digital (135, 210, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 76, 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 (59, 134, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- digital (39, 76, 33)-net over F2, using
(135, 135+75, 86)-Net in Base 2 — Constructive
(135, 210, 86)-net in base 2, using
- trace code for nets [i] based on (30, 105, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
(135, 135+75, 124)-Net over F2 — Digital
Digital (135, 210, 124)-net over F2, using
(135, 135+75, 681)-Net in Base 2 — Upper bound on s
There is no (135, 210, 682)-net in base 2, because
- 1 times m-reduction [i] would yield (135, 209, 682)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 828 071350 916486 952035 989587 188818 984920 360746 701965 080408 541786 > 2209 [i]