MinT - Best Known (105, 105+39, s)-Nets in Base 3

Best Known (105, 105+39, s)-Nets in Base 3

(105, 105+39, 264)-Net over F₃ — Constructive and digital

Digital (105, 144, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 48, 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]

(105, 105+39, 481)-Net over F₃ — Digital

Digital (105, 144, 481)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+39, 15439)-Net in Base 3 — Upper bound on s

There is no (105, 144, 15440)-net in base 3, because

1 times m-reduction [i] would yield (105, 143, 15440)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 297290 994252 813163 197751 581674 927528 866471 333753 610348 164980 459841 > 3¹⁴³ [i]