Best Known (159, 159+64, s)-Nets in Base 2
(159, 159+64, 138)-Net over F2 — Constructive and digital
Digital (159, 223, 138)-net over F2, using
- 21 times duplication [i] based on digital (158, 222, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 74, 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, 74, 46)-net over F8, using
(159, 159+64, 218)-Net over F2 — Digital
Digital (159, 223, 218)-net over F2, using
(159, 159+64, 1555)-Net in Base 2 — Upper bound on s
There is no (159, 223, 1556)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 13 694214 714911 018934 296482 314436 015409 185652 632004 581396 904988 303088 > 2223 [i]