MinT - Best Known (74, 74+29, s)-Nets in Base 3

Best Known (74, 74+29, s)-Nets in Base 3

(74, 74+29, 204)-Net over F₃ — Constructive and digital

Digital (74, 103, 204)-net over F₃, using

3¹ times duplication [i] based on digital (73, 102, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 34, 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]

(74, 74+29, 325)-Net over F₃ — Digital

Digital (74, 103, 325)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+29, 9035)-Net in Base 3 — Upper bound on s

There is no (74, 103, 9036)-net in base 3, because

1 times m-reduction [i] would yield (74, 102, 9036)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 642480 652465 155914 398152 139686 304285 671411 132937 > 3¹⁰² [i]