MinT - Best Known (72, 72+36, s)-Nets in Base 3

Best Known (72, 72+36, s)-Nets in Base 3

(72, 72+36, 148)-Net over F₃ — Constructive and digital

Digital (72, 108, 148)-net over F₃, using

2 times m-reduction [i] based on digital (72, 110, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 55, 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]

(72, 72+36, 191)-Net over F₃ — Digital

Digital (72, 108, 191)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+36, 2735)-Net in Base 3 — Upper bound on s

There is no (72, 108, 2736)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3388 430774 306617 579325 722209 882104 458294 561869 087777 > 3¹⁰⁸ [i]