Best Known (162, 259, s)-Nets in Base 2
(162, 259, 85)-Net over F2 — Constructive and digital
Digital (162, 259, 85)-net over F2, using
- 1 times m-reduction [i] based on digital (162, 260, 85)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (54, 103, 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, 157, 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, 103, 42)-net over F2, using
- (u, u+v)-construction [i] based on
(162, 259, 86)-Net in Base 2 — Constructive
(162, 259, 86)-net in base 2, using
- t-expansion [i] based on (160, 259, 86)-net in base 2, using
- 1 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
- 1 times m-reduction [i] based on (160, 260, 86)-net in base 2, using
(162, 259, 134)-Net over F2 — Digital
Digital (162, 259, 134)-net over F2, using
(162, 259, 709)-Net in Base 2 — Upper bound on s
There is no (162, 259, 710)-net in base 2, because
- 1 times m-reduction [i] would yield (162, 258, 710)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 489942 129255 156019 241778 402895 554653 576764 497395 327108 001299 663230 321337 433460 > 2258 [i]