MinT - Best Known (137−104, 137, s)-Nets in Base 9

Best Known (137−104, 137, s)-Nets in Base 9

(137−104, 137, 81)-Net over F₉ — Constructive and digital

Digital (33, 137, 81)-net over F₉, using

t-expansion [i] based on digital (32, 137, 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]

(137−104, 137, 128)-Net over F₉ — Digital

Digital (33, 137, 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]

(137−104, 137, 794)-Net in Base 9 — Upper bound on s

There is no (33, 137, 795)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 56830 971802 884718 742135 012304 647042 087726 772308 188668 656452 492267 646885 922123 931908 944560 307801 883786 607447 283067 504805 668685 432545 > 9¹³⁷ [i]