MinT - Best Known (142−53, 142, s)-Nets in Base 9

Best Known (142−53, 142, s)-Nets in Base 9

(142−53, 142, 740)-Net over F₉ — Constructive and digital

Digital (89, 142, 740)-net over F₉, using

4 times m-reduction [i] based on digital (89, 146, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 73, 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]

(142−53, 142, 1046)-Net over F₉ — Digital

Digital (89, 142, 1046)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−53, 142, 197287)-Net in Base 9 — Upper bound on s

There is no (89, 142, 197288)-net in base 9, because

1 times m-reduction [i] would yield (89, 141, 197288)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 353 377947 525036 201459 804183 986812 666772 336369 269530 912875 256833 211573 604924 128982 734334 411508 194841 103091 257582 618683 909515 634900 941185 > 9¹⁴¹ [i]