MinT - Best Known (142−68, 142, s)-Nets in Base 9

Best Known (142−68, 142, s)-Nets in Base 9

(142−68, 142, 232)-Net over F₉ — Constructive and digital

Digital (74, 142, 232)-net over F₉, using

2 times m-reduction [i] based on digital (74, 144, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 72, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(142−68, 142, 319)-Net over F₉ — Digital

Digital (74, 142, 319)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−68, 142, 16338)-Net in Base 9 — Upper bound on s

There is no (74, 142, 16339)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3186 357372 396894 434698 450856 118242 876041 712477 938706 367440 669716 491193 706592 408321 088435 416317 104011 546388 828460 954762 621947 719401 549745 > 9¹⁴² [i]