MinT - Best Known (124−59, 124, s)-Nets in Base 8

Best Known (124−59, 124, s)-Nets in Base 8

(124−59, 124, 208)-Net over F₈ — Constructive and digital

Digital (65, 124, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 62, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(124−59, 124, 256)-Net over F₈ — Digital

Digital (65, 124, 256)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−59, 124, 11263)-Net in Base 8 — Upper bound on s

There is no (65, 124, 11264)-net in base 8, because

1 times m-reduction [i] would yield (65, 123, 11264)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1204 066760 463873 824357 987748 979731 904485 322341 243844 830059 166964 796940 170971 799229 539297 246067 894592 565779 315009 > 8¹²³ [i]