MinT - Best Known (84, 84+41, s)-Nets in Base 3

Best Known (84, 84+41, s)-Nets in Base 3

(84, 84+41, 148)-Net over F₃ — Constructive and digital

Digital (84, 125, 148)-net over F₃, using

9 times m-reduction [i] based on digital (84, 134, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 67, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(84, 84+41, 226)-Net over F₃ — Digital

Digital (84, 125, 226)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+41, 3751)-Net in Base 3 — Upper bound on s

There is no (84, 125, 3752)-net in base 3, because

1 times m-reduction [i] would yield (84, 124, 3752)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 146103 507812 947512 906406 039465 335409 033833 743769 567674 070081 > 3¹²⁴ [i]