MinT - Best Known (191−85, 191, s)-Nets in Base 3

Best Known (191−85, 191, s)-Nets in Base 3

(191−85, 191, 80)-Net over F₃ — Constructive and digital

Digital (106, 191, 80)-net over F₃, using

5 times m-reduction [i] based on digital (106, 196, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 98, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(191−85, 191, 133)-Net over F₃ — Digital

Digital (106, 191, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−85, 191, 1148)-Net in Base 3 — Upper bound on s

There is no (106, 191, 1149)-net in base 3, because

1 times m-reduction [i] would yield (106, 190, 1149)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 646581 554272 531160 824719 620880 278089 798157 083225 656428 957465 326948 947843 948002 376572 448161 > 3¹⁹⁰ [i]