MinT - Best Known (114, 159, s)-Nets in Base 3

Best Known (114, 159, s)-Nets in Base 3

(114, 159, 252)-Net over F₃ — Constructive and digital

Digital (114, 159, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 53, 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]

(114, 159, 444)-Net over F₃ — Digital

Digital (114, 159, 444)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 159, 12068)-Net in Base 3 — Upper bound on s

There is no (114, 159, 12069)-net in base 3, because

1 times m-reduction [i] would yield (114, 158, 12069)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2430 269496 771464 305998 362546 676558 648695 710457 616344 775224 701159 955480 806081 > 3¹⁵⁸ [i]