Best Known (205−58, 205, s)-Nets in Base 2
(205−58, 205, 138)-Net over F2 — Constructive and digital
Digital (147, 205, 138)-net over F2, using
- 21 times duplication [i] based on digital (146, 204, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 68, 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, 68, 46)-net over F8, using
(205−58, 205, 209)-Net over F2 — Digital
Digital (147, 205, 209)-net over F2, using
(205−58, 205, 1524)-Net in Base 2 — Upper bound on s
There is no (147, 205, 1525)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 51 787577 103928 069718 094818 014299 257748 289231 577097 807001 785112 > 2205 [i]