MinT - Best Known (154−41, 154, s)-Nets in Base 3

Best Known (154−41, 154, s)-Nets in Base 3

(154−41, 154, 282)-Net over F₃ — Constructive and digital

Digital (113, 154, 282)-net over F₃, using

3¹ times duplication [i] based on digital (112, 153, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 51, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(154−41, 154, 541)-Net over F₃ — Digital

Digital (113, 154, 541)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−41, 154, 18526)-Net in Base 3 — Upper bound on s

There is no (113, 154, 18527)-net in base 3, because

1 times m-reduction [i] would yield (113, 153, 18527)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 993337 568417 665996 982456 067171 617414 333855 243331 230188 677163 206083 481561 > 3¹⁵³ [i]