MinT - Best Known (75, 75+31, s)-Nets in Base 3

Best Known (75, 75+31, s)-Nets in Base 3

(75, 75+31, 192)-Net over F₃ — Constructive and digital

Digital (75, 106, 192)-net over F₃, using

3¹ times duplication [i] based on digital (74, 105, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 35, 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]

(75, 75+31, 289)-Net over F₃ — Digital

Digital (75, 106, 289)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+31, 7009)-Net in Base 3 — Upper bound on s

There is no (75, 106, 7010)-net in base 3, because

1 times m-reduction [i] would yield (75, 105, 7010)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 125 363168 521455 417223 644328 981813 415095 262127 014681 > 3¹⁰⁵ [i]