MinT - Best Known (102−32, 102, s)-Nets in Base 3

Best Known (102−32, 102, s)-Nets in Base 3

(102−32, 102, 148)-Net over F₃ — Constructive and digital

Digital (70, 102, 148)-net over F₃, using

4 times m-reduction [i] based on digital (70, 106, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 53, 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]

(102−32, 102, 221)-Net over F₃ — Digital

Digital (70, 102, 221)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−32, 102, 3726)-Net in Base 3 — Upper bound on s

There is no (70, 102, 3727)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 638734 007713 151335 310733 673952 782320 540162 571745 > 3¹⁰² [i]