MinT - Best Known (209−83, 209, s)-Nets in Base 3

Best Known (209−83, 209, s)-Nets in Base 3

(209−83, 209, 148)-Net over F₃ — Constructive and digital

Digital (126, 209, 148)-net over F₃, using

9 times m-reduction [i] based on digital (126, 218, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 109, 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]

(209−83, 209, 198)-Net over F₃ — Digital

Digital (126, 209, 198)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−83, 209, 2085)-Net in Base 3 — Upper bound on s

There is no (126, 209, 2086)-net in base 3, because

1 times m-reduction [i] would yield (126, 208, 2086)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1775 877247 031486 811380 963735 139754 198521 610155 997241 782328 860370 178775 459283 162439 749331 823030 773117 > 3²⁰⁸ [i]