Best Known (109, 109+39, s)-Nets in Base 2
(109, 109+39, 138)-Net over F2 — Constructive and digital
Digital (109, 148, 138)-net over F2, using
- 21 times duplication [i] based on digital (108, 147, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 49, 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, 49, 46)-net over F8, using
(109, 109+39, 192)-Net over F2 — Digital
Digital (109, 148, 192)-net over F2, using
(109, 109+39, 1663)-Net in Base 2 — Upper bound on s
There is no (109, 148, 1664)-net in base 2, because
- 1 times m-reduction [i] would yield (109, 147, 1664)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 179 263874 452337 338009 604468 185243 931145 547401 > 2147 [i]