MinT - Best Known (191−77, 191, s)-Nets in Base 3

Best Known (191−77, 191, s)-Nets in Base 3

(191−77, 191, 148)-Net over F₃ — Constructive and digital

Digital (114, 191, 148)-net over F₃, using

3 times m-reduction [i] based on digital (114, 194, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 97, 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]

(191−77, 191, 176)-Net over F₃ — Digital

Digital (114, 191, 176)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−77, 191, 1788)-Net in Base 3 — Upper bound on s

There is no (114, 191, 1789)-net in base 3, because

1 times m-reduction [i] would yield (114, 190, 1789)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 563460 241719 270530 543118 438254 604244 875852 765486 369077 498022 743848 214420 980763 679062 195825 > 3¹⁹⁰ [i]