MinT - Best Known (151−63, 151, s)-Nets in Base 3

Best Known (151−63, 151, s)-Nets in Base 3

(151−63, 151, 80)-Net over F₃ — Constructive and digital

Digital (88, 151, 80)-net over F₃, using

9 times m-reduction [i] based on digital (88, 160, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 80, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(151−63, 151, 130)-Net over F₃ — Digital

Digital (88, 151, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−63, 151, 1233)-Net in Base 3 — Upper bound on s

There is no (88, 151, 1234)-net in base 3, because

1 times m-reduction [i] would yield (88, 150, 1234)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 374249 659702 435646 076799 340531 239149 830442 186766 530466 640622 724764 567225 > 3¹⁵⁰ [i]