MinT - Best Known (84, 114, s)-Nets in Base 3

Best Known (84, 114, s)-Nets in Base 3

(84, 114, 252)-Net over F₃ — Constructive and digital

Digital (84, 114, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 38, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(84, 114, 452)-Net over F₃ — Digital

Digital (84, 114, 452)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 114, 13564)-Net in Base 3 — Upper bound on s

There is no (84, 114, 13565)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 467197 437334 709444 454432 117079 140469 828443 396363 225691 > 3¹¹⁴ [i]