MinT - Best Known (119, 119+83, s)-Nets in Base 3

Best Known (119, 119+83, s)-Nets in Base 3

(119, 119+83, 148)-Net over F₃ — Constructive and digital

Digital (119, 202, 148)-net over F₃, using

2 times m-reduction [i] based on digital (119, 204, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 102, 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]

(119, 119+83, 175)-Net over F₃ — Digital

Digital (119, 202, 175)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+83, 1721)-Net in Base 3 — Upper bound on s

There is no (119, 202, 1722)-net in base 3, because

1 times m-reduction [i] would yield (119, 201, 1722)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 803929 925699 587826 468350 027232 115108 892385 059288 754569 069831 611588 833471 045067 355442 086888 835685 > 3²⁰¹ [i]