MinT - Best Known (82, 82+45, s)-Nets in Base 3

Best Known (82, 82+45, s)-Nets in Base 3

(82, 82+45, 148)-Net over F₃ — Constructive and digital

Digital (82, 127, 148)-net over F₃, using

3 times m-reduction [i] based on digital (82, 130, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 65, 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]

(82, 82+45, 181)-Net over F₃ — Digital

Digital (82, 127, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+45, 2424)-Net in Base 3 — Upper bound on s

There is no (82, 127, 2425)-net in base 3, because

1 times m-reduction [i] would yield (82, 126, 2425)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 316985 363453 758121 620907 876892 052581 386954 960391 522678 625481 > 3¹²⁶ [i]