MinT - Best Known (99, 150, s)-Nets in Base 9

Best Known (99, 150, s)-Nets in Base 9

(99, 150, 740)-Net over F₉ — Constructive and digital

Digital (99, 150, 740)-net over F₉, using

t-expansion [i] based on digital (91, 150, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 75, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(99, 150, 1800)-Net over F₉ — Digital

Digital (99, 150, 1800)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 150, 619170)-Net in Base 9 — Upper bound on s

There is no (99, 150, 619171)-net in base 9, because

1 times m-reduction [i] would yield (99, 149, 619171)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15210 181344 722108 895362 601461 814518 304770 937787 380061 855818 466488 812827 694348 478401 370099 885920 263344 506508 841427 967584 254826 874015 526872 871257 > 9¹⁴⁹ [i]