MinT - Best Known (142, 198, s)-Nets in Base 3

Best Known (142, 198, s)-Nets in Base 3

(142, 198, 282)-Net over F₃ — Constructive and digital

Digital (142, 198, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 66, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(142, 198, 534)-Net over F₃ — Digital

Digital (142, 198, 534)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 198, 13335)-Net in Base 3 — Upper bound on s

There is no (142, 198, 13336)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29542 256127 186862 513511 088287 551161 866555 095582 809430 088614 876951 966379 489610 958765 120894 284993 > 3¹⁹⁸ [i]