Best Known (104, 104+43, s)-Nets in Base 2
(104, 104+43, 84)-Net over F2 — Constructive and digital
Digital (104, 147, 84)-net over F2, using
- t-expansion [i] based on digital (103, 147, 84)-net over F2, using
- trace code for nets [i] based on digital (5, 49, 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, 49, 28)-net over F8, using
(104, 104+43, 86)-Net in Base 2 — Constructive
(104, 147, 86)-net in base 2, using
- 1 times m-reduction [i] based on (104, 148, 86)-net in base 2, using
- trace code for nets [i] based on (30, 74, 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, 74, 43)-net in base 4, using
(104, 104+43, 147)-Net over F2 — Digital
Digital (104, 147, 147)-net over F2, using
(104, 104+43, 1044)-Net in Base 2 — Upper bound on s
There is no (104, 147, 1045)-net in base 2, because
- 1 times m-reduction [i] would yield (104, 146, 1045)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 90 430689 297919 502935 618211 126945 008952 205962 > 2146 [i]