Best Known (133, 133+69, s)-Nets in Base 2
(133, 133+69, 76)-Net over F2 — Constructive and digital
Digital (133, 202, 76)-net over F2, using
- 1 times m-reduction [i] based on digital (133, 203, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 74, 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, 129, 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, 74, 33)-net over F2, using
- (u, u+v)-construction [i] based on
(133, 133+69, 86)-Net in Base 2 — Constructive
(133, 202, 86)-net in base 2, using
- 4 times m-reduction [i] based on (133, 206, 86)-net in base 2, using
- trace code for nets [i] based on (30, 103, 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
- trace code for nets [i] based on (30, 103, 43)-net in base 4, using
(133, 133+69, 133)-Net over F2 — Digital
Digital (133, 202, 133)-net over F2, using
(133, 133+69, 765)-Net in Base 2 — Upper bound on s
There is no (133, 202, 766)-net in base 2, because
- 1 times m-reduction [i] would yield (133, 201, 766)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3 245515 024347 421006 856753 339465 897852 874062 969779 028366 367870 > 2201 [i]