MinT - Best Known (159−69, 159, s)-Nets in Base 8

Best Known (159−69, 159, s)-Nets in Base 8

(159−69, 159, 354)-Net over F₈ — Constructive and digital

Digital (90, 159, 354)-net over F₈, using

7 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 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]

(159−69, 159, 464)-Net over F₈ — Digital

Digital (90, 159, 464)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−69, 159, 30393)-Net in Base 8 — Upper bound on s

There is no (90, 159, 30394)-net in base 8, because

1 times m-reduction [i] would yield (90, 158, 30394)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48789 438557 719549 126080 633695 997795 700633 861622 284926 187473 198588 238608 414815 632993 334328 329736 740176 746768 675042 862071 600399 097535 554962 919396 > 8¹⁵⁸ [i]