Best Known (117, 117+43, s)-Nets in Base 2
(117, 117+43, 138)-Net over F2 — Constructive and digital
Digital (117, 160, 138)-net over F2, using
- 21 times duplication [i] based on digital (116, 159, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 53, 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, 53, 46)-net over F8, using
(117, 117+43, 194)-Net over F2 — Digital
Digital (117, 160, 194)-net over F2, using
(117, 117+43, 1620)-Net in Base 2 — Upper bound on s
There is no (117, 160, 1621)-net in base 2, because
- 1 times m-reduction [i] would yield (117, 159, 1621)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 738614 226355 631522 651137 471677 952234 492608 673442 > 2159 [i]