MinT - Best Known (195−81, 195, s)-Nets in Base 3

Best Known (195−81, 195, s)-Nets in Base 3

(195−81, 195, 128)-Net over F₃ — Constructive and digital

Digital (114, 195, 128)-net over F₃, using

7 times m-reduction [i] based on digital (114, 202, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 101, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(195−81, 195, 164)-Net over F₃ — Digital

Digital (114, 195, 164)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−81, 195, 1585)-Net in Base 3 — Upper bound on s

There is no (114, 195, 1586)-net in base 3, because

1 times m-reduction [i] would yield (114, 194, 1586)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 367 118732 266695 064990 995686 958146 818326 629074 703928 704211 413056 597835 151539 494418 636826 988689 > 3¹⁹⁴ [i]