MinT - Best Known (153, 153+47, s)-Nets in Base 3

Best Known (153, 153+47, s)-Nets in Base 3

(153, 153+47, 464)-Net over F₃ — Constructive and digital

Digital (153, 200, 464)-net over F₃, using

t-expansion [i] based on digital (152, 200, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 50, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(153, 153+47, 1091)-Net over F₃ — Digital

Digital (153, 200, 1091)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+47, 63300)-Net in Base 3 — Upper bound on s

There is no (153, 200, 63301)-net in base 3, because

1 times m-reduction [i] would yield (153, 199, 63301)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88549 864088 244966 182278 248924 255287 146945 126393 345399 934881 872969 225172 516809 471188 528659 557147 > 3¹⁹⁹ [i]