MinT - Best Known (82, 82+61, s)-Nets in Base 3

Best Known (82, 82+61, s)-Nets in Base 3

(82, 82+61, 80)-Net over F₃ — Constructive and digital

Digital (82, 143, 80)-net over F₃, using

5 times m-reduction [i] based on digital (82, 148, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 74, 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]

(82, 82+61, 117)-Net over F₃ — Digital

Digital (82, 143, 117)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+61, 1062)-Net in Base 3 — Upper bound on s

There is no (82, 143, 1063)-net in base 3, because

1 times m-reduction [i] would yield (82, 142, 1063)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57 012553 303174 431006 394665 755478 584719 260725 230082 275625 682444 527829 > 3¹⁴² [i]