MinT - Best Known (119, 119+81, s)-Nets in Base 3

Best Known (119, 119+81, s)-Nets in Base 3

(119, 119+81, 148)-Net over F₃ — Constructive and digital

Digital (119, 200, 148)-net over F₃, using

4 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+81, 180)-Net over F₃ — Digital

Digital (119, 200, 180)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+81, 1824)-Net in Base 3 — Upper bound on s

There is no (119, 200, 1825)-net in base 3, because

1 times m-reduction [i] would yield (119, 199, 1825)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88885 729858 118714 654379 228036 682699 772571 697014 760424 512739 864653 756771 843081 622314 853901 041697 > 3¹⁹⁹ [i]