Best Known (232−67, 232, s)-Nets in Base 2
(232−67, 232, 138)-Net over F2 — Constructive and digital
Digital (165, 232, 138)-net over F2, using
- 21 times duplication [i] based on digital (164, 231, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 77, 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, 77, 46)-net over F8, using
(232−67, 232, 222)-Net over F2 — Digital
Digital (165, 232, 222)-net over F2, using
(232−67, 232, 1636)-Net in Base 2 — Upper bound on s
There is no (165, 232, 1637)-net in base 2, because
- 1 times m-reduction [i] would yield (165, 231, 1637)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3484 604374 054844 027961 618038 200020 508537 376888 413480 003380 116642 796650 > 2231 [i]