MinT - Best Known (65, 65+36, s)-Nets in Base 3

Best Known (65, 65+36, s)-Nets in Base 3

(65, 65+36, 128)-Net over F₃ — Constructive and digital

Digital (65, 101, 128)-net over F₃, using

3 times m-reduction [i] based on digital (65, 104, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 52, 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]

(65, 65+36, 149)-Net over F₃ — Digital

Digital (65, 101, 149)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+36, 1778)-Net in Base 3 — Upper bound on s

There is no (65, 101, 1779)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 554461 484914 143666 678685 592003 419057 511220 934245 > 3¹⁰¹ [i]