Best Known (142−39, 142, s)-Nets in Base 2
(142−39, 142, 105)-Net over F2 — Constructive and digital
Digital (103, 142, 105)-net over F2, using
- 21 times duplication [i] based on digital (102, 141, 105)-net over F2, using
- trace code for nets [i] based on digital (8, 47, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- trace code for nets [i] based on digital (8, 47, 35)-net over F8, using
(142−39, 142, 167)-Net over F2 — Digital
Digital (103, 142, 167)-net over F2, using
(142−39, 142, 1331)-Net in Base 2 — Upper bound on s
There is no (103, 142, 1332)-net in base 2, because
- 1 times m-reduction [i] would yield (103, 141, 1332)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 822085 796361 366656 224822 167600 402850 962545 > 2141 [i]