MinT - Best Known (72, 72+35, s)-Nets in Base 3

Best Known (72, 72+35, s)-Nets in Base 3

(72, 72+35, 148)-Net over F₃ — Constructive and digital

Digital (72, 107, 148)-net over F₃, using

3 times m-reduction [i] based on digital (72, 110, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 55, 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]

(72, 72+35, 201)-Net over F₃ — Digital

Digital (72, 107, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+35, 3371)-Net in Base 3 — Upper bound on s

There is no (72, 107, 3372)-net in base 3, because

1 times m-reduction [i] would yield (72, 106, 3372)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 377 133949 381794 739691 714740 622653 323735 186714 545241 > 3¹⁰⁶ [i]