Best Known (129, 129+65, s)-Nets in Base 2
(129, 129+65, 76)-Net over F2 — Constructive and digital
Digital (129, 194, 76)-net over F2, using
- 21 times duplication [i] based on digital (128, 193, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (42, 74, 34)-net over F2, using
- trace code for nets [i] based on digital (5, 37, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- trace code for nets [i] based on digital (5, 37, 17)-net over F4, using
- digital (54, 119, 42)-net over F2, using
- net from sequence [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
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (42, 74, 34)-net over F2, using
- (u, u+v)-construction [i] based on
(129, 129+65, 86)-Net in Base 2 — Constructive
(129, 194, 86)-net in base 2, using
- 4 times m-reduction [i] based on (129, 198, 86)-net in base 2, using
- trace code for nets [i] based on (30, 99, 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, 99, 43)-net in base 4, using
(129, 129+65, 135)-Net over F2 — Digital
Digital (129, 194, 135)-net over F2, using
(129, 129+65, 790)-Net in Base 2 — Upper bound on s
There is no (129, 194, 791)-net in base 2, because
- 1 times m-reduction [i] would yield (129, 193, 791)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 12944 876902 451377 391879 917650 044851 841465 598178 109572 794680 > 2193 [i]