Best Known (138−52, 138, s)-Nets in Base 2
(138−52, 138, 66)-Net over F2 — Constructive and digital
Digital (86, 138, 66)-net over F2, using
- 4 times m-reduction [i] based on digital (86, 142, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 71, 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, 71, 33)-net over F4, using
(138−52, 138, 80)-Net over F2 — Digital
Digital (86, 138, 80)-net over F2, using
- trace code for nets [i] based on digital (17, 69, 40)-net over F4, using
- net from sequence [i] based on digital (17, 39)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 17 and N(F) ≥ 40, using
- net from sequence [i] based on digital (17, 39)-sequence over F4, using
(138−52, 138, 380)-Net in Base 2 — Upper bound on s
There is no (86, 138, 381)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 349839 380335 942369 890750 059998 100142 004714 > 2138 [i]