Best Known (209−59, 209, s)-Nets in Base 2
(209−59, 209, 138)-Net over F2 — Constructive and digital
Digital (150, 209, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (150, 210, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 70, 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, 70, 46)-net over F8, using
(209−59, 209, 214)-Net over F2 — Digital
Digital (150, 209, 214)-net over F2, using
(209−59, 209, 1641)-Net in Base 2 — Upper bound on s
There is no (150, 209, 1642)-net in base 2, because
- 1 times m-reduction [i] would yield (150, 208, 1642)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 417 980362 576665 928281 961826 030706 528141 965559 639229 669736 104136 > 2208 [i]