MinT - Best Known (209−93, 209, s)-Nets in Base 3

Best Known (209−93, 209, s)-Nets in Base 3

(209−93, 209, 80)-Net over F₃ — Constructive and digital

Digital (116, 209, 80)-net over F₃, using

7 times m-reduction [i] based on digital (116, 216, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 108, 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]

(209−93, 209, 144)-Net over F₃ — Digital

Digital (116, 209, 144)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−93, 209, 1248)-Net in Base 3 — Upper bound on s

There is no (116, 209, 1249)-net in base 3, because

1 times m-reduction [i] would yield (116, 208, 1249)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1792 234864 663490 983589 769890 770390 578595 480609 230748 434733 459790 745031 574421 545798 554279 101436 570809 > 3²⁰⁸ [i]