MinT - Best Known (91, 160, s)-Nets in Base 8

Best Known (91, 160, s)-Nets in Base 8

(91, 160, 354)-Net over F₈ — Constructive and digital

Digital (91, 160, 354)-net over F₈, using

8 times m-reduction [i] based on digital (91, 168, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 84, 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]

(91, 160, 480)-Net over F₈ — Digital

Digital (91, 160, 480)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 160, 32312)-Net in Base 8 — Upper bound on s

There is no (91, 160, 32313)-net in base 8, because

1 times m-reduction [i] would yield (91, 159, 32313)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390616 545662 271770 312970 000620 417629 902950 148469 032602 571731 560183 542927 177673 840712 617149 471384 496538 073203 664178 483180 622376 181926 114067 966876 > 8¹⁵⁹ [i]