MinT - Best Known (191−79, 191, s)-Nets in Base 3

Best Known (191−79, 191, s)-Nets in Base 3

(191−79, 191, 128)-Net over F₃ — Constructive and digital

Digital (112, 191, 128)-net over F₃, using

7 times m-reduction [i] based on digital (112, 198, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 99, 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]

(191−79, 191, 163)-Net over F₃ — Digital

Digital (112, 191, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−79, 191, 1586)-Net in Base 3 — Upper bound on s

There is no (112, 191, 1587)-net in base 3, because

1 times m-reduction [i] would yield (112, 190, 1587)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 520221 757898 075193 413346 598369 096082 081273 102627 898037 403732 741766 247168 493616 017537 522051 > 3¹⁹⁰ [i]