MinT - Best Known (37, 136, s)-Nets in Base 9

Best Known (37, 136, s)-Nets in Base 9

(37, 136, 81)-Net over F₉ — Constructive and digital

Digital (37, 136, 81)-net over F₉, using

t-expansion [i] based on digital (32, 136, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(37, 136, 128)-Net over F₉ — Digital

Digital (37, 136, 128)-net over F₉, using

t-expansion [i] based on digital (33, 136, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(37, 136, 986)-Net in Base 9 — Upper bound on s

There is no (37, 136, 987)-net in base 9, because

1 times m-reduction [i] would yield (37, 135, 987)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 665 655712 106265 193104 615672 303705 115992 979975 486893 192432 257343 795343 803230 345105 958872 362653 718943 068727 114685 775662 669513 859929 > 9¹³⁵ [i]