MinT - Best Known (142−65, 142, s)-Nets in Base 3

Best Known (142−65, 142, s)-Nets in Base 3

(142−65, 142, 68)-Net over F₃ — Constructive and digital

Digital (77, 142, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 71, 34)-net over F₉, using
- net from sequence [i] based on digital (6, 33)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(142−65, 142, 96)-Net over F₃ — Digital

Digital (77, 142, 96)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−65, 142, 778)-Net in Base 3 — Upper bound on s

There is no (77, 142, 779)-net in base 3, because

1 times m-reduction [i] would yield (77, 141, 779)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19 243866 822323 365524 182308 801458 889603 515569 704093 962809 293024 723905 > 3¹⁴¹ [i]