MinT - Best Known (191−71, 191, s)-Nets in Base 3

Best Known (191−71, 191, s)-Nets in Base 3

(191−71, 191, 156)-Net over F₃ — Constructive and digital

Digital (120, 191, 156)-net over F₃, using

5 times m-reduction [i] based on digital (120, 196, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 98, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(191−71, 191, 221)-Net over F₃ — Digital

Digital (120, 191, 221)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−71, 191, 2671)-Net in Base 3 — Upper bound on s

There is no (120, 191, 2672)-net in base 3, because

1 times m-reduction [i] would yield (120, 190, 2672)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 519327 292127 973365 433542 653070 214766 512723 073095 357408 399176 597081 889669 112269 893936 127425 > 3¹⁹⁰ [i]