Best Known (209−132, 209, s)-Nets in Base 2
(209−132, 209, 50)-Net over F2 — Constructive and digital
Digital (77, 209, 50)-net over F2, using
- t-expansion [i] based on digital (75, 209, 50)-net over F2, using
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
(209−132, 209, 52)-Net over F2 — Digital
Digital (77, 209, 52)-net over F2, using
- net from sequence [i] based on digital (77, 51)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 77 and N(F) ≥ 52, using
(209−132, 209, 145)-Net in Base 2 — Upper bound on s
There is no (77, 209, 146)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 931 653220 435047 369907 016900 364586 836773 843413 098483 979597 332768 > 2209 [i]