Best Known (158, 158+63, s)-Nets in Base 2
(158, 158+63, 138)-Net over F2 — Constructive and digital
Digital (158, 221, 138)-net over F2, using
- 1 times m-reduction [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
(158, 158+63, 220)-Net over F2 — Digital
Digital (158, 221, 220)-net over F2, using
(158, 158+63, 1654)-Net in Base 2 — Upper bound on s
There is no (158, 221, 1655)-net in base 2, because
- 1 times m-reduction [i] would yield (158, 220, 1655)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 707529 212527 764067 551916 608373 630856 823966 883087 877594 826294 394376 > 2220 [i]