Best Known (142−37, 142, s)-Nets in Base 2
(142−37, 142, 138)-Net over F2 — Constructive and digital
Digital (105, 142, 138)-net over F2, using
- 21 times duplication [i] based on digital (104, 141, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 47, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- trace code for nets [i] based on digital (10, 47, 46)-net over F8, using
(142−37, 142, 192)-Net over F2 — Digital
Digital (105, 142, 192)-net over F2, using
(142−37, 142, 1696)-Net in Base 2 — Upper bound on s
There is no (105, 142, 1697)-net in base 2, because
- 1 times m-reduction [i] would yield (105, 141, 1697)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 806911 241026 056843 676170 478955 724033 978440 > 2141 [i]