Best Known (100, 100+40, s)-Nets in Base 2
(100, 100+40, 84)-Net over F2 — Constructive and digital
Digital (100, 140, 84)-net over F2, using
- t-expansion [i] based on digital (99, 140, 84)-net over F2, using
- 1 times m-reduction [i] based on digital (99, 141, 84)-net over F2, using
- trace code for nets [i] based on digital (5, 47, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- trace code for nets [i] based on digital (5, 47, 28)-net over F8, using
- 1 times m-reduction [i] based on digital (99, 141, 84)-net over F2, using
(100, 100+40, 86)-Net in Base 2 — Constructive
(100, 140, 86)-net in base 2, using
- trace code for nets [i] based on (30, 70, 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
(100, 100+40, 150)-Net over F2 — Digital
Digital (100, 140, 150)-net over F2, using
(100, 100+40, 1033)-Net in Base 2 — Upper bound on s
There is no (100, 140, 1034)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 398382 261338 269333 628266 312277 776950 041728 > 2140 [i]