MinT - Best Known (67, 67+59, s)-Nets in Base 8

Best Known (67, 67+59, s)-Nets in Base 8

(67, 67+59, 208)-Net over F₈ — Constructive and digital

Digital (67, 126, 208)-net over F₈, using

2 times m-reduction [i] based on digital (67, 128, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 64, 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]

(67, 67+59, 277)-Net over F₈ — Digital

Digital (67, 126, 277)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+59, 13003)-Net in Base 8 — Upper bound on s

There is no (67, 126, 13004)-net in base 8, because

1 times m-reduction [i] would yield (67, 125, 13004)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 77105 974134 222496 442316 807025 670784 030615 112907 922790 633416 806556 510240 073986 002435 499733 542230 837186 897893 464624 > 8¹²⁵ [i]