MinT - Best Known (67, 67+27, s)-Nets in Base 3

Best Known (67, 67+27, s)-Nets in Base 3

(67, 67+27, 192)-Net over F₃ — Constructive and digital

Digital (67, 94, 192)-net over F₃, using

3¹ times duplication [i] based on digital (66, 93, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 31, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(67, 67+27, 283)-Net over F₃ — Digital

Digital (67, 94, 283)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+27, 7326)-Net in Base 3 — Upper bound on s

There is no (67, 94, 7327)-net in base 3, because

1 times m-reduction [i] would yield (67, 93, 7327)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 235 921185 038052 917851 546394 418088 475463 091239 > 3⁹³ [i]