MinT - Best Known (71, 71+33, s)-Nets in Base 3

Best Known (71, 71+33, s)-Nets in Base 3

(71, 71+33, 148)-Net over F₃ — Constructive and digital

Digital (71, 104, 148)-net over F₃, using

4 times m-reduction [i] based on digital (71, 108, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 54, 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]

(71, 71+33, 216)-Net over F₃ — Digital

Digital (71, 104, 216)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+33, 3992)-Net in Base 3 — Upper bound on s

There is no (71, 104, 3993)-net in base 3, because

1 times m-reduction [i] would yield (71, 103, 3993)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 916406 880528 532695 543904 345665 550046 718448 239425 > 3¹⁰³ [i]