MinT - Best Known (191−60, 191, s)-Nets in Base 3

Best Known (191−60, 191, s)-Nets in Base 3

(191−60, 191, 164)-Net over F₃ — Constructive and digital

Digital (131, 191, 164)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 37, 16)-net over F₃, using
  - net from sequence [i] based on digital (7, 15)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, using
      - an explicitly constructive algebraic function field [i]
2. digital (94, 154, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 77, 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]

(191−60, 191, 369)-Net over F₃ — Digital

Digital (131, 191, 369)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−60, 191, 6538)-Net in Base 3 — Upper bound on s

There is no (131, 191, 6539)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 524348 971941 468815 271106 705442 678498 389866 868571 470769 008355 869462 195064 323057 516175 701885 > 3¹⁹¹ [i]