MinT - Best Known (167, 167+75, s)-Nets in Base 3

Best Known (167, 167+75, s)-Nets in Base 3

(167, 167+75, 204)-Net over F₃ — Constructive and digital

Digital (167, 242, 204)-net over F₃, using

1 times m-reduction [i] based on digital (167, 243, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 81, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(167, 167+75, 473)-Net over F₃ — Digital

Digital (167, 242, 473)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+75, 9352)-Net in Base 3 — Upper bound on s

There is no (167, 242, 9353)-net in base 3, because

1 times m-reduction [i] would yield (167, 241, 9353)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 706060 927161 855823 441444 298195 617623 113283 761908 422348 640933 915685 875877 419639 838299 521668 846107 585677 156325 341443 > 3²⁴¹ [i]