MinT - Best Known (246−55, 246, s)-Nets in Base 3

Best Known (246−55, 246, s)-Nets in Base 3

(246−55, 246, 640)-Net over F₃ — Constructive and digital

Digital (191, 246, 640)-net over F₃, using

2 times m-reduction [i] based on digital (191, 248, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 62, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(246−55, 246, 1590)-Net over F₃ — Digital

Digital (191, 246, 1590)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−55, 246, 116603)-Net in Base 3 — Upper bound on s

There is no (191, 246, 116604)-net in base 3, because

1 times m-reduction [i] would yield (191, 245, 116604)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 784 791969 805592 317820 584517 306871 275951 321036 671763 137605 311733 763123 921398 746718 819676 486676 361201 349227 031078 605137 > 3²⁴⁵ [i]