MinT - Best Known (143−67, 143, s)-Nets in Base 9

Best Known (143−67, 143, s)-Nets in Base 9

(143−67, 143, 300)-Net over F₉ — Constructive and digital

Digital (76, 143, 300)-net over F₉, using

1 times m-reduction [i] based on digital (76, 144, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 72, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(143−67, 143, 352)-Net over F₉ — Digital

Digital (76, 143, 352)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−67, 143, 20988)-Net in Base 9 — Upper bound on s

There is no (76, 143, 20989)-net in base 9, because

1 times m-reduction [i] would yield (76, 142, 20989)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3182 312675 582273 036571 325479 962553 797554 762677 990360 670621 546510 920351 334375 471770 691640 733704 420787 499079 793964 499065 353348 253436 311785 > 9¹⁴² [i]