MinT - Best Known (99, 99+49, s)-Nets in Base 9

Best Known (99, 99+49, s)-Nets in Base 9

(99, 99+49, 740)-Net over F₉ — Constructive and digital

Digital (99, 148, 740)-net over F₉, using

t-expansion [i] based on digital (91, 148, 740)-net over F₉, using
- 2 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+49, 2075)-Net over F₉ — Digital

Digital (99, 148, 2075)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+49, 857039)-Net in Base 9 — Upper bound on s

There is no (99, 148, 857040)-net in base 9, because

1 times m-reduction [i] would yield (99, 147, 857040)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 187 783126 546061 663641 709649 303996 697230 213997 802569 953163 958675 529606 293470 080596 196009 324395 430298 902225 243959 051218 815967 227259 618760 483841 > 9¹⁴⁷ [i]