MinT - Best Known (248−78, 248, s)-Nets in Base 3

Best Known (248−78, 248, s)-Nets in Base 3

(248−78, 248, 192)-Net over F₃ — Constructive and digital

Digital (170, 248, 192)-net over F₃, using

1 times m-reduction [i] based on digital (170, 249, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 83, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(248−78, 248, 461)-Net over F₃ — Digital

Digital (170, 248, 461)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−78, 248, 8286)-Net in Base 3 — Upper bound on s

There is no (170, 248, 8287)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21204 915920 879602 700499 853591 467327 499711 550939 582270 891492 764242 949916 547072 604842 619982 236177 466199 805013 505940 280115 > 3²⁴⁸ [i]