MinT - Best Known (85−37, 85, s)-Nets in Base 8

Best Known (85−37, 85, s)-Nets in Base 8

(85−37, 85, 256)-Net over F₈ — Constructive and digital

Digital (48, 85, 256)-net over F₈, using

1 times m-reduction [i] based on digital (48, 86, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 43, 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]

(85−37, 85, 275)-Net over F₈ — Digital

Digital (48, 85, 275)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−37, 85, 17667)-Net in Base 8 — Upper bound on s

There is no (48, 85, 17668)-net in base 8, because

1 times m-reduction [i] would yield (48, 84, 17668)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7239 237880 729459 475394 254922 361720 469174 652749 662172 689518 018169 200442 712720 > 8⁸⁴ [i]