MinT - Best Known (160−61, 160, s)-Nets in Base 3

Best Known (160−61, 160, s)-Nets in Base 3

(160−61, 160, 148)-Net over F₃ — Constructive and digital

Digital (99, 160, 148)-net over F₃, using

4 times m-reduction [i] based on digital (99, 164, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 82, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(160−61, 160, 177)-Net over F₃ — Digital

Digital (99, 160, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−61, 160, 2005)-Net in Base 3 — Upper bound on s

There is no (99, 160, 2006)-net in base 3, because

1 times m-reduction [i] would yield (99, 159, 2006)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7349 172062 136240 646463 061397 772588 254333 869812 706623 126416 386406 500716 664805 > 3¹⁵⁹ [i]