MinT - Best Known (140−66, 140, s)-Nets in Base 8

Best Known (140−66, 140, s)-Nets in Base 8

(140−66, 140, 208)-Net over F₈ — Constructive and digital

Digital (74, 140, 208)-net over F₈, using

2 times m-reduction [i] based on digital (74, 142, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 71, 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]

(140−66, 140, 294)-Net over F₈ — Digital

Digital (74, 140, 294)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−66, 140, 12730)-Net in Base 8 — Upper bound on s

There is no (74, 140, 12731)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 712070 467379 846324 427183 977766 898587 290605 147132 407641 654879 002380 255685 330018 478973 594585 340393 697812 458441 950189 300693 732210 > 8¹⁴⁰ [i]