MinT - Best Known (87, 87+53, s)-Nets in Base 3

Best Known (87, 87+53, s)-Nets in Base 3

(87, 87+53, 148)-Net over F₃ — Constructive and digital

Digital (87, 140, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 70, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(87, 87+53, 161)-Net over F₃ — Digital

Digital (87, 140, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+53, 1849)-Net in Base 3 — Upper bound on s

There is no (87, 140, 1850)-net in base 3, because

1 times m-reduction [i] would yield (87, 139, 1850)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 095744 695032 882820 874554 018231 025559 688944 436363 971664 577265 778069 > 3¹³⁹ [i]