MinT - Best Known (107−31, 107, s)-Nets in Base 3

Best Known (107−31, 107, s)-Nets in Base 3

(107−31, 107, 192)-Net over F₃ — Constructive and digital

Digital (76, 107, 192)-net over F₃, using

1 times m-reduction [i] based on digital (76, 108, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 36, 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]

(107−31, 107, 301)-Net over F₃ — Digital

Digital (76, 107, 301)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−31, 107, 7543)-Net in Base 3 — Upper bound on s

There is no (76, 107, 7544)-net in base 3, because

1 times m-reduction [i] would yield (76, 106, 7544)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 376 248304 440872 391025 642016 072119 504079 180791 085985 > 3¹⁰⁶ [i]