MinT - Best Known (107−27, 107, s)-Nets in Base 3

Best Known (107−27, 107, s)-Nets in Base 3

(107−27, 107, 252)-Net over F₃ — Constructive and digital

Digital (80, 107, 252)-net over F₃, using

1 times m-reduction [i] based on digital (80, 108, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 36, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(107−27, 107, 498)-Net over F₃ — Digital

Digital (80, 107, 498)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−27, 107, 22004)-Net in Base 3 — Upper bound on s

There is no (80, 107, 22005)-net in base 3, because

1 times m-reduction [i] would yield (80, 106, 22005)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 375 917834 143919 827668 395935 554135 779158 783224 325339 > 3¹⁰⁶ [i]