MinT - Best Known (105−45, 105, s)-Nets in Base 3

Best Known (105−45, 105, s)-Nets in Base 3

(105−45, 105, 72)-Net over F₃ — Constructive and digital

Digital (60, 105, 72)-net over F₃, using

1 times m-reduction [i] based on digital (60, 106, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 53, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]

(105−45, 105, 90)-Net over F₃ — Digital

Digital (60, 105, 90)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−45, 105, 794)-Net in Base 3 — Upper bound on s

There is no (60, 105, 795)-net in base 3, because

1 times m-reduction [i] would yield (60, 104, 795)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42 874246 699387 571067 028480 272503 425947 475940 682093 > 3¹⁰⁴ [i]