MinT - Best Known (169−75, 169, s)-Nets in Base 3

Best Known (169−75, 169, s)-Nets in Base 3

(169−75, 169, 80)-Net over F₃ — Constructive and digital

Digital (94, 169, 80)-net over F₃, using

3 times m-reduction [i] based on digital (94, 172, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 86, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(169−75, 169, 121)-Net over F₃ — Digital

Digital (94, 169, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−75, 169, 1038)-Net in Base 3 — Upper bound on s

There is no (94, 169, 1039)-net in base 3, because

1 times m-reduction [i] would yield (94, 168, 1039)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 144 999937 874894 920019 784759 902224 375401 432431 249133 297335 549631 920043 240845 361495 > 3¹⁶⁸ [i]