Best Known (226−65, 226, s)-Nets in Base 2
(226−65, 226, 138)-Net over F2 — Constructive and digital
Digital (161, 226, 138)-net over F2, using
- 21 times duplication [i] based on digital (160, 225, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 75, 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, 75, 46)-net over F8, using
(226−65, 226, 219)-Net over F2 — Digital
Digital (161, 226, 219)-net over F2, using
(226−65, 226, 1626)-Net in Base 2 — Upper bound on s
There is no (161, 226, 1627)-net in base 2, because
- 1 times m-reduction [i] would yield (161, 225, 1627)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 54 841338 530563 219862 221763 401319 503879 026271 207057 449125 343996 692522 > 2225 [i]