MinT - Best Known (84−25, 84, s)-Nets in Base 3

Best Known (84−25, 84, s)-Nets in Base 3

(84−25, 84, 156)-Net over F₃ — Constructive and digital

Digital (59, 84, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 28, 52)-net over F₂₇, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by SÃ©mirat [i]

(84−25, 84, 231)-Net over F₃ — Digital

Digital (59, 84, 231)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−25, 84, 5265)-Net in Base 3 — Upper bound on s

There is no (59, 84, 5266)-net in base 3, because

1 times m-reduction [i] would yield (59, 83, 5266)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3991 641435 420754 764359 783639 016434 204793 > 3⁸³ [i]