MinT - Best Known (145−49, 145, s)-Nets in Base 9

Best Known (145−49, 145, s)-Nets in Base 9

(145−49, 145, 740)-Net over F₉ — Constructive and digital

Digital (96, 145, 740)-net over F₉, using

t-expansion [i] based on digital (91, 145, 740)-net over F₉, using
- 5 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]

(145−49, 145, 1812)-Net over F₉ — Digital

Digital (96, 145, 1812)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−49, 145, 651205)-Net in Base 9 — Upper bound on s

There is no (96, 145, 651206)-net in base 9, because

1 times m-reduction [i] would yield (96, 144, 651206)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 257589 133290 760908 860470 957068 489351 907606 053831 201351 225157 528613 974059 179317 537726 378286 763179 245986 795644 939825 622701 871209 749033 033089 > 9¹⁴⁴ [i]