MinT - Best Known (64, 64+60, s)-Nets in Base 8

Best Known (64, 64+60, s)-Nets in Base 8

(64, 64+60, 160)-Net over F₈ — Constructive and digital

Digital (64, 124, 160)-net over F₈, using

2 times m-reduction [i] based on digital (64, 126, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 63, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(64, 64+60, 238)-Net over F₈ — Digital

Digital (64, 124, 238)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+60, 9280)-Net in Base 8 — Upper bound on s

There is no (64, 124, 9281)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9626 159355 307338 591427 182764 183548 891771 519061 668110 825372 945924 206475 814272 348677 116411 093097 653396 443890 658720 > 8¹²⁴ [i]