MinT - Best Known (134, 134+62, s)-Nets in Base 3

Best Known (134, 134+62, s)-Nets in Base 3

(134, 134+62, 164)-Net over F₃ — Constructive and digital

Digital (134, 196, 164)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 38, 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 (96, 158, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 79, 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]

(134, 134+62, 369)-Net over F₃ — Digital

Digital (134, 196, 369)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+62, 6420)-Net in Base 3 — Upper bound on s

There is no (134, 196, 6421)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3282 951261 336326 565949 844827 115899 450130 977984 029143 480785 890484 597118 912954 367017 447893 832955 > 3¹⁹⁶ [i]