MinT - Best Known (99−47, 99, s)-Nets in Base 8

Best Known (99−47, 99, s)-Nets in Base 8

(99−47, 99, 160)-Net over F₈ — Constructive and digital

Digital (52, 99, 160)-net over F₈, using

3 times m-reduction [i] based on digital (52, 102, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 51, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(99−47, 99, 214)-Net over F₈ — Digital

Digital (52, 99, 214)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−47, 99, 9476)-Net in Base 8 — Upper bound on s

There is no (52, 99, 9477)-net in base 8, because

1 times m-reduction [i] would yield (52, 98, 9477)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 31858 810698 149156 652921 340152 556317 804788 655870 026892 312774 885817 589169 305932 334854 894336 > 8⁹⁸ [i]