MinT - Best Known (206−49, 206, s)-Nets in Base 3

Best Known (206−49, 206, s)-Nets in Base 3

(206−49, 206, 464)-Net over F₃ — Constructive and digital

Digital (157, 206, 464)-net over F₃, using

3² times duplication [i] based on digital (155, 204, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 51, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(206−49, 206, 1065)-Net over F₃ — Digital

Digital (157, 206, 1065)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−49, 206, 58286)-Net in Base 3 — Upper bound on s

There is no (157, 206, 58287)-net in base 3, because

1 times m-reduction [i] would yield (157, 205, 58287)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 555892 240840 064174 781951 858448 093772 241319 951613 248809 906893 086696 218032 902021 621269 030002 387153 > 3²⁰⁵ [i]