MinT - Best Known (78−31, 78, s)-Nets in Base 3

Best Known (78−31, 78, s)-Nets in Base 3

(78−31, 78, 80)-Net over F₃ — Constructive and digital

Digital (47, 78, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 39, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(78−31, 78, 89)-Net over F₃ — Digital

Digital (47, 78, 89)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−31, 78, 889)-Net in Base 3 — Upper bound on s

There is no (47, 78, 890)-net in base 3, because

1 times m-reduction [i] would yield (47, 77, 890)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 551154 639190 086613 825020 773778 259001 > 3⁷⁷ [i]