MinT - Best Known (222−91, 222, s)-Nets in Base 3

Best Known (222−91, 222, s)-Nets in Base 3

(222−91, 222, 148)-Net over F₃ — Constructive and digital

Digital (131, 222, 148)-net over F₃, using

6 times m-reduction [i] based on digital (131, 228, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 114, 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]

(222−91, 222, 191)-Net over F₃ — Digital

Digital (131, 222, 191)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−91, 222, 1898)-Net in Base 3 — Upper bound on s

There is no (131, 222, 1899)-net in base 3, because

1 times m-reduction [i] would yield (131, 221, 1899)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2822 399420 624603 903633 599721 544769 023684 677990 194509 687460 628081 905219 276721 750019 649054 672880 250131 160063 > 3²²¹ [i]