MinT - Best Known (64, 64+42, s)-Nets in Base 3

Best Known (64, 64+42, s)-Nets in Base 3

(64, 64+42, 80)-Net over F₃ — Constructive and digital

Digital (64, 106, 80)-net over F₃, using

6 times m-reduction [i] based on digital (64, 112, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 56, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(64, 64+42, 113)-Net over F₃ — Digital

Digital (64, 106, 113)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+42, 1090)-Net in Base 3 — Upper bound on s

There is no (64, 106, 1091)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 376 790137 182652 050723 967532 269468 413218 324680 048479 > 3¹⁰⁶ [i]