MinT - Best Known (151−45, 151, s)-Nets in Base 3

Best Known (151−45, 151, s)-Nets in Base 3

(151−45, 151, 204)-Net over F₃ — Constructive and digital

Digital (106, 151, 204)-net over F₃, using

3¹ times duplication [i] based on digital (105, 150, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 50, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(151−45, 151, 357)-Net over F₃ — Digital

Digital (106, 151, 357)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−45, 151, 8086)-Net in Base 3 — Upper bound on s

There is no (106, 151, 8087)-net in base 3, because

1 times m-reduction [i] would yield (106, 150, 8087)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 370302 560511 633581 661164 377087 931320 914891 592615 112815 558804 586804 935749 > 3¹⁵⁰ [i]