MinT - Best Known (176, 176+53, s)-Nets in Base 3

Best Known (176, 176+53, s)-Nets in Base 3

(176, 176+53, 600)-Net over F₃ — Constructive and digital

Digital (176, 229, 600)-net over F₃, using

3¹ times duplication [i] based on digital (175, 228, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 57, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(176, 176+53, 1302)-Net over F₃ — Digital

Digital (176, 229, 1302)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 176+53, 80558)-Net in Base 3 — Upper bound on s

There is no (176, 229, 80559)-net in base 3, because

1 times m-reduction [i] would yield (176, 228, 80559)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 077147 726032 398226 007097 206196 474678 732025 222930 854515 651769 690257 748237 312362 193386 561119 280227 645567 104813 > 3²²⁸ [i]