Best Known (162−51, 162, s)-Nets in Base 2
(162−51, 162, 75)-Net over F2 — Constructive and digital
Digital (111, 162, 75)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (5, 30, 9)-net over F2, using
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 5 and N(F) ≥ 9, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- digital (81, 132, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 66, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- trace code for nets [i] based on digital (15, 66, 33)-net over F4, using
- digital (5, 30, 9)-net over F2, using
(162−51, 162, 86)-Net in Base 2 — Constructive
(111, 162, 86)-net in base 2, using
- trace code for nets [i] based on (30, 81, 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
(162−51, 162, 134)-Net over F2 — Digital
Digital (111, 162, 134)-net over F2, using
(162−51, 162, 847)-Net in Base 2 — Upper bound on s
There is no (111, 162, 848)-net in base 2, because
- 1 times m-reduction [i] would yield (111, 161, 848)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 981645 888418 204414 598183 111145 642745 074134 866060 > 2161 [i]