MinT - Best Known (135−60, 135, s)-Nets in Base 8

Best Known (135−60, 135, s)-Nets in Base 8

(135−60, 135, 354)-Net over F₈ — Constructive and digital

Digital (75, 135, 354)-net over F₈, using

1 times m-reduction [i] based on digital (75, 136, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 68, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(135−60, 135, 364)-Net over F₈ — Digital

Digital (75, 135, 364)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−60, 135, 19915)-Net in Base 8 — Upper bound on s

There is no (75, 135, 19916)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 82 722703 572926 137476 554640 977387 090496 549430 637171 485181 603620 369595 286565 979273 216717 263195 862396 589405 292509 149217 508240 > 8¹³⁵ [i]