MinT - Best Known (69, 132, s)-Nets in Base 8

Best Known (69, 132, s)-Nets in Base 8

(69, 132, 208)-Net over F₈ — Constructive and digital

Digital (69, 132, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 66, 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]

(69, 132, 266)-Net over F₈ — Digital

Digital (69, 132, 266)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 132, 11600)-Net in Base 8 — Upper bound on s

There is no (69, 132, 11601)-net in base 8, because

1 times m-reduction [i] would yield (69, 131, 11601)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20178 665129 801666 031405 674296 694463 984387 547326 112061 221605 875701 814804 063806 290915 081667 268917 927107 584257 053510 724544 > 8¹³¹ [i]