MinT - Best Known (73, 106, s)-Nets in Base 3

Best Known (73, 106, s)-Nets in Base 3

(73, 106, 148)-Net over F₃ — Constructive and digital

Digital (73, 106, 148)-net over F₃, using

6 times m-reduction [i] based on digital (73, 112, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 56, 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]

(73, 106, 233)-Net over F₃ — Digital

Digital (73, 106, 233)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 106, 4583)-Net in Base 3 — Upper bound on s

There is no (73, 106, 4584)-net in base 3, because

1 times m-reduction [i] would yield (73, 105, 4584)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 125 660075 461986 845642 150961 307922 080362 508904 987649 > 3¹⁰⁵ [i]