MinT - Best Known (84−38, 84, s)-Nets in Base 3

Best Known (84−38, 84, s)-Nets in Base 3

(84−38, 84, 60)-Net over F₃ — Constructive and digital

Digital (46, 84, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 42, 30)-net over F₉, using
- net from sequence [i] based on digital (4, 29)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
    - a function field by SÃ©mirat [i]

(84−38, 84, 65)-Net over F₃ — Digital

Digital (46, 84, 65)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−38, 84, 491)-Net in Base 3 — Upper bound on s

There is no (46, 84, 492)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 12076 538741 998808 749773 030146 509497 633105 > 3⁸⁴ [i]