Best Known (227−65, 227, s)-Nets in Base 2
(227−65, 227, 138)-Net over F2 — Constructive and digital
Digital (162, 227, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (162, 228, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 76, 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, 76, 46)-net over F8, using
(227−65, 227, 222)-Net over F2 — Digital
Digital (162, 227, 222)-net over F2, using
(227−65, 227, 1662)-Net in Base 2 — Upper bound on s
There is no (162, 227, 1663)-net in base 2, because
- 1 times m-reduction [i] would yield (162, 226, 1663)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 108 375284 749235 903187 776326 772248 218972 722935 552797 717272 864287 096101 > 2226 [i]