MinT - Best Known (90, 146, s)-Nets in Base 3

Best Known (90, 146, s)-Nets in Base 3

(90, 146, 148)-Net over F₃ — Constructive and digital

Digital (90, 146, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 73, 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]

(90, 146, 161)-Net over F₃ — Digital

Digital (90, 146, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 146, 1709)-Net in Base 3 — Upper bound on s

There is no (90, 146, 1710)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4584 917149 370202 263261 784655 023050 625552 019618 608673 065308 568741 003129 > 3¹⁴⁶ [i]