MinT - Best Known (136−37, 136, s)-Nets in Base 3

Best Known (136−37, 136, s)-Nets in Base 3

(136−37, 136, 252)-Net over F₃ — Constructive and digital

Digital (99, 136, 252)-net over F₃, using

3¹ times duplication [i] based on digital (98, 135, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 45, 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]

(136−37, 136, 453)-Net over F₃ — Digital

Digital (99, 136, 453)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−37, 136, 14288)-Net in Base 3 — Upper bound on s

There is no (99, 136, 14289)-net in base 3, because

1 times m-reduction [i] would yield (99, 135, 14289)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25810 427256 082960 272462 949662 785370 737430 579983 813661 727635 475305 > 3¹³⁵ [i]