MinT - Best Known (37, 37+74, s)-Nets in Base 9

Best Known (37, 37+74, s)-Nets in Base 9

(37, 37+74, 81)-Net over F₉ — Constructive and digital

Digital (37, 111, 81)-net over F₉, using

t-expansion [i] based on digital (32, 111, 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, 37+74, 128)-Net over F₉ — Digital

Digital (37, 111, 128)-net over F₉, using

t-expansion [i] based on digital (33, 111, 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, 37+74, 1312)-Net in Base 9 — Upper bound on s

There is no (37, 111, 1313)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8405 671983 783021 087674 922678 855600 457907 865390 727751 600463 242436 139385 390637 401052 794033 810406 638785 089705 > 9¹¹¹ [i]