MinT - Best Known (72, 72+62, s)-Nets in Base 3

Best Known (72, 72+62, s)-Nets in Base 3

(72, 72+62, 64)-Net over F₃ — Constructive and digital

Digital (72, 134, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 67, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(72, 72+62, 89)-Net over F₃ — Digital

Digital (72, 134, 89)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+62, 686)-Net in Base 3 — Upper bound on s

There is no (72, 134, 687)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8658 564160 357639 601035 516670 301483 199167 762808 877963 434673 572995 > 3¹³⁴ [i]