MinT - Best Known (163, 163+51, s)-Nets in Base 3

Best Known (163, 163+51, s)-Nets in Base 3

(163, 163+51, 464)-Net over F₃ — Constructive and digital

Digital (163, 214, 464)-net over F₃, using

3² times duplication [i] based on digital (161, 212, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 53, 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]

(163, 163+51, 1090)-Net over F₃ — Digital

Digital (163, 214, 1090)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+51, 59086)-Net in Base 3 — Upper bound on s

There is no (163, 214, 59087)-net in base 3, because

1 times m-reduction [i] would yield (163, 213, 59087)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423548 291458 096220 504169 328594 781495 430062 972303 148914 977627 078386 027266 452386 433908 190761 524950 196079 > 3²¹³ [i]