MinT - Best Known (174, 227, s)-Nets in Base 3

Best Known (174, 227, s)-Nets in Base 3

(174, 227, 464)-Net over F₃ — Constructive and digital

Digital (174, 227, 464)-net over F₃, using

t-expansion [i] based on digital (173, 227, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (173, 228, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 57, 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]

(174, 227, 1246)-Net over F₃ — Digital

Digital (174, 227, 1246)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 227, 74028)-Net in Base 3 — Upper bound on s

There is no (174, 227, 74029)-net in base 3, because

1 times m-reduction [i] would yield (174, 226, 74029)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 675302 107940 123692 862863 257901 771406 762432 155401 005172 891229 074460 683481 278827 380154 865889 121229 735181 661505 > 3²²⁶ [i]