MinT - Best Known (63, 116, s)-Nets in Base 8

Best Known (63, 116, s)-Nets in Base 8

(63, 116, 256)-Net over F₈ — Constructive and digital

Digital (63, 116, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 58, 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]

(63, 116, 285)-Net over F₈ — Digital

Digital (63, 116, 285)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 116, 14864)-Net in Base 8 — Upper bound on s

There is no (63, 116, 14865)-net in base 8, because

1 times m-reduction [i] would yield (63, 115, 14865)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 71 700718 518883 347081 362297 774477 475952 687697 611470 068348 922624 413475 958350 063656 747195 426061 428215 542016 > 8¹¹⁵ [i]