MinT - Best Known (104, 104+67, s)-Nets in Base 3

Best Known (104, 104+67, s)-Nets in Base 3

(104, 104+67, 148)-Net over F₃ — Constructive and digital

Digital (104, 171, 148)-net over F₃, using

3 times m-reduction [i] based on digital (104, 174, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 87, 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]

(104, 104+67, 173)-Net over F₃ — Digital

Digital (104, 171, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+67, 1856)-Net in Base 3 — Upper bound on s

There is no (104, 171, 1857)-net in base 3, because

1 times m-reduction [i] would yield (104, 170, 1857)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1297 170024 721811 174176 940611 292846 405454 937855 855461 752882 098136 360145 264862 198275 > 3¹⁷⁰ [i]