MinT - Best Known (73, 73+37, s)-Nets in Base 3

Best Known (73, 73+37, s)-Nets in Base 3

(73, 73+37, 148)-Net over F₃ — Constructive and digital

Digital (73, 110, 148)-net over F₃, using

2 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, 73+37, 189)-Net over F₃ — Digital

Digital (73, 110, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+37, 2908)-Net in Base 3 — Upper bound on s

There is no (73, 110, 2909)-net in base 3, because

1 times m-reduction [i] would yield (73, 109, 2909)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10147 423047 728807 755828 891952 178491 903367 722666 390785 > 3¹⁰⁹ [i]