MinT - Best Known (152−41, 152, s)-Nets in Base 3

Best Known (152−41, 152, s)-Nets in Base 3

(152−41, 152, 264)-Net over F₃ — Constructive and digital

Digital (111, 152, 264)-net over F₃, using

1 times m-reduction [i] based on digital (111, 153, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 51, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(152−41, 152, 509)-Net over F₃ — Digital

Digital (111, 152, 509)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−41, 152, 16597)-Net in Base 3 — Upper bound on s

There is no (111, 152, 16598)-net in base 3, because

1 times m-reduction [i] would yield (111, 151, 16598)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 111179 046598 189351 713962 489960 232166 311177 726365 561163 808557 701252 784041 > 3¹⁵¹ [i]