MinT - Best Known (99, 99+47, s)-Nets in Base 9

Best Known (99, 99+47, s)-Nets in Base 9

(99, 99+47, 740)-Net over F₉ — Constructive and digital

Digital (99, 146, 740)-net over F₉, using

t-expansion [i] based on digital (91, 146, 740)-net over F₉, using
- 4 times m-reduction [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, 99+47, 2426)-Net over F₉ — Digital

Digital (99, 146, 2426)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+47, 1222469)-Net in Base 9 — Upper bound on s

There is no (99, 146, 1222470)-net in base 9, because

1 times m-reduction [i] would yield (99, 145, 1222470)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 318288 477455 301558 390721 781298 153152 553547 236442 185040 617639 336397 045991 079771 257125 872961 052795 762404 143387 227806 768173 690959 721810 461329 > 9¹⁴⁵ [i]