Best Known (161, 161+97, s)-Nets in Base 2
(161, 161+97, 85)-Net over F2 — Constructive and digital
Digital (161, 258, 85)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (54, 102, 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 (59, 156, 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 (54, 102, 42)-net over F2, using
(161, 161+97, 86)-Net in Base 2 — Constructive
(161, 258, 86)-net in base 2, using
- t-expansion [i] based on (160, 258, 86)-net in base 2, using
- 2 times m-reduction [i] based on (160, 260, 86)-net in base 2, using
- trace code for nets [i] based on (30, 130, 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, 130, 43)-net in base 4, using
- 2 times m-reduction [i] based on (160, 260, 86)-net in base 2, using
(161, 161+97, 132)-Net over F2 — Digital
Digital (161, 258, 132)-net over F2, using
(161, 161+97, 697)-Net in Base 2 — Upper bound on s
There is no (161, 258, 698)-net in base 2, because
- 1 times m-reduction [i] would yield (161, 257, 698)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 231851 817805 758059 989981 965079 211070 243258 105841 761432 237477 289650 431623 379607 > 2257 [i]