MinT - Best Known (146−48, 146, s)-Nets in Base 9

Best Known (146−48, 146, s)-Nets in Base 9

(146−48, 146, 740)-Net over F₉ — Constructive and digital

Digital (98, 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]

(146−48, 146, 2138)-Net over F₉ — Digital

Digital (98, 146, 2138)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−48, 146, 782059)-Net in Base 9 — Upper bound on s

There is no (98, 146, 782060)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 864550 516076 626165 229915 341410 537731 645208 053921 605444 555729 443956 309281 914447 673179 382006 493249 266198 282895 280122 982598 746925 310682 547969 > 9¹⁴⁶ [i]