MinT - Best Known (120−41, 120, s)-Nets in Base 9

Best Known (120−41, 120, s)-Nets in Base 9

(120−41, 120, 740)-Net over F₉ — Constructive and digital

Digital (79, 120, 740)-net over F₉, using

6 times m-reduction [i] based on digital (79, 126, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 63, 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]

(120−41, 120, 1457)-Net over F₉ — Digital

Digital (79, 120, 1457)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−41, 120, 494252)-Net in Base 9 — Upper bound on s

There is no (79, 120, 494253)-net in base 9, because

1 times m-reduction [i] would yield (79, 119, 494253)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 358816 400581 422631 544763 457488 780042 407694 229958 914585 248977 926705 785336 923358 211234 513561 363134 668378 069354 606241 > 9¹¹⁹ [i]