MinT - Best Known (38, 120, s)-Nets in Base 9

Best Known (38, 120, s)-Nets in Base 9

(38, 120, 81)-Net over F₉ — Constructive and digital

Digital (38, 120, 81)-net over F₉, using

t-expansion [i] based on digital (32, 120, 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]

(38, 120, 128)-Net over F₉ — Digital

Digital (38, 120, 128)-net over F₉, using

t-expansion [i] based on digital (33, 120, 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]

(38, 120, 1227)-Net in Base 9 — Upper bound on s

There is no (38, 120, 1228)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 295685 211115 289464 522560 903842 597941 262802 596357 668283 377087 295934 499162 249686 003308 948250 228400 744548 578873 293665 > 9¹²⁰ [i]