MinT - Best Known (192−45, 192, s)-Nets in Base 3

Best Known (192−45, 192, s)-Nets in Base 3

(192−45, 192, 464)-Net over F₃ — Constructive and digital

Digital (147, 192, 464)-net over F₃, using

t-expansion [i] based on digital (146, 192, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 48, 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]

(192−45, 192, 1064)-Net over F₃ — Digital

Digital (147, 192, 1064)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−45, 192, 62799)-Net in Base 3 — Upper bound on s

There is no (147, 192, 62800)-net in base 3, because

1 times m-reduction [i] would yield (147, 191, 62800)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 498188 421394 848542 574727 481370 972575 133159 127573 737201 830382 980352 236978 130610 446912 218081 > 3¹⁹¹ [i]