MinT - Best Known (116−55, 116, s)-Nets in Base 8

Best Known (116−55, 116, s)-Nets in Base 8

(116−55, 116, 208)-Net over F₈ — Constructive and digital

Digital (61, 116, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 58, 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]

(116−55, 116, 245)-Net over F₈ — Digital

Digital (61, 116, 245)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−55, 116, 10942)-Net in Base 8 — Upper bound on s

There is no (61, 116, 10943)-net in base 8, because

1 times m-reduction [i] would yield (61, 115, 10943)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 71 678326 916583 361998 686911 546729 313476 614046 989155 729759 934271 508176 160399 586416 815378 483715 270057 700884 > 8¹¹⁵ [i]