MinT - Best Known (155, 155+76, s)-Nets in Base 3

Best Known (155, 155+76, s)-Nets in Base 3

(155, 155+76, 164)-Net over F₃ — Constructive and digital

Digital (155, 231, 164)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 45, 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 (110, 186, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 93, 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]

(155, 155+76, 375)-Net over F₃ — Digital

Digital (155, 231, 375)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 155+76, 5935)-Net in Base 3 — Upper bound on s

There is no (155, 231, 5936)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 833567 299935 631864 214151 113059 860603 676327 539830 146321 389779 737035 247081 700857 654744 266823 421279 314387 836193 > 3²³¹ [i]