MinT - Best Known (133, 133+103, s)-Nets in Base 3

Best Known (133, 133+103, s)-Nets in Base 3

(133, 133+103, 128)-Net over F₃ — Constructive and digital

Digital (133, 236, 128)-net over F₃, using

4 times m-reduction [i] based on digital (133, 240, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 120, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(133, 133+103, 169)-Net over F₃ — Digital

Digital (133, 236, 169)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+103, 1518)-Net in Base 3 — Upper bound on s

There is no (133, 236, 1519)-net in base 3, because

1 times m-reduction [i] would yield (133, 235, 1519)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13686 971857 444764 419116 483487 857853 465685 180949 508264 506930 302808 109040 328260 547156 236904 541880 704375 338761 812571 > 3²³⁵ [i]