MinT - Best Known (95, 95+49, s)-Nets in Base 9

Best Known (95, 95+49, s)-Nets in Base 9

(95, 95+49, 740)-Net over F₉ — Constructive and digital

Digital (95, 144, 740)-net over F₉, using

t-expansion [i] based on digital (91, 144, 740)-net over F₉, using
- 6 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]

(95, 95+49, 1732)-Net over F₉ — Digital

Digital (95, 144, 1732)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(95, 95+49, 594233)-Net in Base 9 — Upper bound on s

There is no (95, 144, 594234)-net in base 9, because

1 times m-reduction [i] would yield (95, 143, 594234)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28621 228806 375835 535059 516452 672320 266503 070233 776804 022876 795725 252241 889207 731372 945357 200945 031154 788447 831992 450853 982179 471660 037761 > 9¹⁴³ [i]