MinT - Best Known (107−47, 107, s)-Nets in Base 3

Best Known (107−47, 107, s)-Nets in Base 3

(107−47, 107, 68)-Net over F₃ — Constructive and digital

Digital (60, 107, 68)-net over F₃, using

1 times m-reduction [i] based on digital (60, 108, 68)-net over F₃, using
- trace code for nets [i] based on digital (6, 54, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(107−47, 107, 85)-Net over F₃ — Digital

Digital (60, 107, 85)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−47, 107, 723)-Net in Base 3 — Upper bound on s

There is no (60, 107, 724)-net in base 3, because

1 times m-reduction [i] would yield (60, 106, 724)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 386 496474 149430 282274 664251 091082 811579 800672 486705 > 3¹⁰⁶ [i]