MinT - Best Known (76−33, 76, s)-Nets in Base 8

Best Known (76−33, 76, s)-Nets in Base 8

(76−33, 76, 256)-Net over F₈ — Constructive and digital

Digital (43, 76, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 38, 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]

(76−33, 76, 266)-Net over F₈ — Digital

Digital (43, 76, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 38, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(76−33, 76, 16611)-Net in Base 8 — Upper bound on s

There is no (43, 76, 16612)-net in base 8, because

1 times m-reduction [i] would yield (43, 75, 16612)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 925124 072188 628123 448320 305521 280324 054901 495284 698295 841092 900490 > 8⁷⁵ [i]