MinT - Best Known (77, 77+67, s)-Nets in Base 9

Best Known (77, 77+67, s)-Nets in Base 9

(77, 77+67, 320)-Net over F₉ — Constructive and digital

Digital (77, 144, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 72, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(77, 77+67, 365)-Net over F₉ — Digital

Digital (77, 144, 365)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+67, 22434)-Net in Base 9 — Upper bound on s

There is no (77, 144, 22435)-net in base 9, because

1 times m-reduction [i] would yield (77, 143, 22435)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28621 423265 469181 837344 689063 468094 199796 014954 731232 872838 932528 930701 362124 003022 491756 028018 291665 701627 718031 821951 943303 361786 214425 > 9¹⁴³ [i]