MinT - Best Known (135, 135+93, s)-Nets in Base 3

Best Known (135, 135+93, s)-Nets in Base 3

(135, 135+93, 148)-Net over F₃ — Constructive and digital

Digital (135, 228, 148)-net over F₃, using

8 times m-reduction [i] based on digital (135, 236, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 118, 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]

(135, 135+93, 198)-Net over F₃ — Digital

Digital (135, 228, 198)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+93, 1990)-Net in Base 3 — Upper bound on s

There is no (135, 228, 1991)-net in base 3, because

1 times m-reduction [i] would yield (135, 227, 1991)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 048240 479774 004299 581600 140322 789749 912300 916440 204098 962000 392029 724565 529800 732690 988725 450694 033332 522229 > 3²²⁷ [i]