MinT - Best Known (205−91, 205, s)-Nets in Base 3

Best Known (205−91, 205, s)-Nets in Base 3

(205−91, 205, 80)-Net over F₃ — Constructive and digital

Digital (114, 205, 80)-net over F₃, using

7 times m-reduction [i] based on digital (114, 212, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 106, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(205−91, 205, 143)-Net over F₃ — Digital

Digital (114, 205, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−91, 205, 1238)-Net in Base 3 — Upper bound on s

There is no (114, 205, 1239)-net in base 3, because

1 times m-reduction [i] would yield (114, 204, 1239)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 713332 935553 316609 660651 794085 675010 458234 872763 867277 359386 181687 529403 676311 367534 258144 628759 > 3²⁰⁴ [i]