MinT - Best Known (150, 150+65, s)-Nets in Base 3

Best Known (150, 150+65, s)-Nets in Base 3

(150, 150+65, 228)-Net over F₃ — Constructive and digital

Digital (150, 215, 228)-net over F₃, using

1 times m-reduction [i] based on digital (150, 216, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 72, 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]

(150, 150+65, 460)-Net over F₃ — Digital

Digital (150, 215, 460)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+65, 9890)-Net in Base 3 — Upper bound on s

There is no (150, 215, 9891)-net in base 3, because

1 times m-reduction [i] would yield (150, 214, 9891)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 272345 728151 683205 912605 171323 749606 622371 688779 379849 054625 004972 629473 589002 403836 289167 164431 709633 > 3²¹⁴ [i]