MinT - Best Known (138−63, 138, s)-Nets in Base 9

Best Known (138−63, 138, s)-Nets in Base 9

(138−63, 138, 320)-Net over F₉ — Constructive and digital

Digital (75, 138, 320)-net over F₉, using

2 times m-reduction [i] based on digital (75, 140, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 70, 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]

(138−63, 138, 382)-Net over F₉ — Digital

Digital (75, 138, 382)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−63, 138, 25571)-Net in Base 9 — Upper bound on s

There is no (75, 138, 25572)-net in base 9, because

1 times m-reduction [i] would yield (75, 137, 25572)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 53877 180732 284902 995540 282508 975569 098650 658555 952646 669194 076526 379211 050711 991104 182339 208718 940327 109477 769219 757384 179586 970465 > 9¹³⁷ [i]