MinT - Best Known (208−47, 208, s)-Nets in Base 3

Best Known (208−47, 208, s)-Nets in Base 3

(208−47, 208, 640)-Net over F₃ — Constructive and digital

Digital (161, 208, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 52, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(208−47, 208, 1316)-Net over F₃ — Digital

Digital (161, 208, 1316)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−47, 208, 92771)-Net in Base 3 — Upper bound on s

There is no (161, 208, 92772)-net in base 3, because

1 times m-reduction [i] would yield (161, 207, 92772)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 581 040834 216189 998636 351724 559928 024159 797917 714716 682596 532950 810661 199631 685206 804948 116486 990321 > 3²⁰⁷ [i]