MinT - Best Known (142−65, 142, s)-Nets in Base 9

Best Known (142−65, 142, s)-Nets in Base 9

(142−65, 142, 320)-Net over F₉ — Constructive and digital

Digital (77, 142, 320)-net over F₉, using

2 times m-reduction [i] based on digital (77, 144, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 72, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(142−65, 142, 387)-Net over F₉ — Digital

Digital (77, 142, 387)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−65, 142, 25591)-Net in Base 9 — Upper bound on s

There is no (77, 142, 25592)-net in base 9, because

1 times m-reduction [i] would yield (77, 141, 25592)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 353 692562 796512 923010 260441 167217 394619 369546 752152 659088 378365 930239 059086 170478 547635 211958 289099 508810 046247 518266 348673 226707 339265 > 9¹⁴¹ [i]