MinT - Best Known (89, 89+55, s)-Nets in Base 3

Best Known (89, 89+55, s)-Nets in Base 3

(89, 89+55, 148)-Net over F₃ — Constructive and digital

Digital (89, 144, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 72, 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]

(89, 89+55, 161)-Net over F₃ — Digital

Digital (89, 144, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+55, 1811)-Net in Base 3 — Upper bound on s

There is no (89, 144, 1812)-net in base 3, because

1 times m-reduction [i] would yield (89, 143, 1812)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 955323 364684 173223 381604 129650 237605 515221 865498 490498 004419 781297 > 3¹⁴³ [i]