Best Known (145−44, 145, s)-Nets in Base 2
(145−44, 145, 75)-Net over F2 — Constructive and digital
Digital (101, 145, 75)-net over F2, using
- 21 times duplication [i] based on digital (100, 144, 75)-net over F2, using
- trace code for nets [i] based on digital (4, 48, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- trace code for nets [i] based on digital (4, 48, 25)-net over F8, using
(145−44, 145, 84)-Net in Base 2 — Constructive
(101, 145, 84)-net in base 2, using
- 3 times m-reduction [i] based on (101, 148, 84)-net in base 2, using
- trace code for nets [i] based on (27, 74, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [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
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- trace code for nets [i] based on (27, 74, 42)-net in base 4, using
(145−44, 145, 133)-Net over F2 — Digital
Digital (101, 145, 133)-net over F2, using
(145−44, 145, 840)-Net in Base 2 — Upper bound on s
There is no (101, 145, 841)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 44 781903 405938 253030 743906 393396 840270 834928 > 2145 [i]