MinT - Best Known (117, 117+81, s)-Nets in Base 3

Best Known (117, 117+81, s)-Nets in Base 3

(117, 117+81, 148)-Net over F₃ — Constructive and digital

Digital (117, 198, 148)-net over F₃, using

2 times m-reduction [i] based on digital (117, 200, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 100, 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]

(117, 117+81, 174)-Net over F₃ — Digital

Digital (117, 198, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+81, 1725)-Net in Base 3 — Upper bound on s

There is no (117, 198, 1726)-net in base 3, because

1 times m-reduction [i] would yield (117, 197, 1726)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10015 592321 363871 011581 343058 027693 070847 455396 575984 647291 431791 127619 188403 926628 435591 006097 > 3¹⁹⁷ [i]