MinT - Best Known (72, 72+43, s)-Nets in Base 3

Best Known (72, 72+43, s)-Nets in Base 3

(72, 72+43, 128)-Net over F₃ — Constructive and digital

Digital (72, 115, 128)-net over F₃, using

3 times m-reduction [i] based on digital (72, 118, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 59, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(72, 72+43, 143)-Net over F₃ — Digital

Digital (72, 115, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+43, 1668)-Net in Base 3 — Upper bound on s

There is no (72, 115, 1669)-net in base 3, because

1 times m-reduction [i] would yield (72, 114, 1669)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 486852 265906 730782 600931 665176 301532 890267 336319 659227 > 3¹¹⁴ [i]