MinT - Best Known (82, 82+43, s)-Nets in Base 3

Best Known (82, 82+43, s)-Nets in Base 3

(82, 82+43, 148)-Net over F₃ — Constructive and digital

Digital (82, 125, 148)-net over F₃, using

5 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+43, 197)-Net over F₃ — Digital

Digital (82, 125, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+43, 2828)-Net in Base 3 — Upper bound on s

There is no (82, 125, 2829)-net in base 3, because

1 times m-reduction [i] would yield (82, 124, 2829)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145623 397559 254565 763779 862890 559150 952355 185439 448481 263339 > 3¹²⁴ [i]