MinT - Best Known (245−109, 245, s)-Nets in Base 3

Best Known (245−109, 245, s)-Nets in Base 3

(245−109, 245, 128)-Net over F₃ — Constructive and digital

Digital (136, 245, 128)-net over F₃, using

1 times m-reduction [i] based on digital (136, 246, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 123, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(245−109, 245, 166)-Net over F₃ — Digital

Digital (136, 245, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−109, 245, 1448)-Net in Base 3 — Upper bound on s

There is no (136, 245, 1449)-net in base 3, because

1 times m-reduction [i] would yield (136, 244, 1449)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 267 985755 129530 130573 140640 028072 333809 191963 388088 082608 177703 498084 965723 307375 805992 275281 384804 584175 028051 032361 > 3²⁴⁴ [i]