MinT - Best Known (142−41, 142, s)-Nets in Base 3

Best Known (142−41, 142, s)-Nets in Base 3

(142−41, 142, 228)-Net over F₃ — Constructive and digital

Digital (101, 142, 228)-net over F₃, using

3¹ times duplication [i] based on digital (100, 141, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 47, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(142−41, 142, 378)-Net over F₃ — Digital

Digital (101, 142, 378)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−41, 142, 9574)-Net in Base 3 — Upper bound on s

There is no (101, 142, 9575)-net in base 3, because

1 times m-reduction [i] would yield (101, 141, 9575)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 832468 190773 130709 244677 760037 965152 909037 255029 121102 508348 184921 > 3¹⁴¹ [i]