MinT - Best Known (165−77, 165, s)-Nets in Base 8

Best Known (165−77, 165, s)-Nets in Base 8

(165−77, 165, 256)-Net over F₈ — Constructive and digital

Digital (88, 165, 256)-net over F₈, using

1 times m-reduction [i] based on digital (88, 166, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 83, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(165−77, 165, 353)-Net over F₈ — Digital

Digital (88, 165, 353)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−77, 165, 16929)-Net in Base 8 — Upper bound on s

There is no (88, 165, 16930)-net in base 8, because

1 times m-reduction [i] would yield (88, 164, 16930)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12807 615484 932419 772512 925890 946652 756914 915155 834068 417214 377726 505189 523937 365361 463713 455773 190040 514787 684912 398561 786507 060253 508414 345721 114368 > 8¹⁶⁴ [i]