MinT - Best Known (82, 82+60, s)-Nets in Base 8

Best Known (82, 82+60, s)-Nets in Base 8

(82, 82+60, 354)-Net over F₈ — Constructive and digital

Digital (82, 142, 354)-net over F₈, using

8 times m-reduction [i] based on digital (82, 150, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 75, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(82, 82+60, 474)-Net over F₈ — Digital

Digital (82, 142, 474)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+60, 32364)-Net in Base 8 — Upper bound on s

There is no (82, 142, 32365)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 423637 211354 050442 622063 491359 622965 360971 527692 262045 375804 011731 699377 277190 671622 162310 054149 719592 183595 090334 892431 928432 > 8¹⁴² [i]