MinT - Best Known (34, 145, s)-Nets in Base 9

Best Known (34, 145, s)-Nets in Base 9

(34, 145, 81)-Net over F₉ — Constructive and digital

Digital (34, 145, 81)-net over F₉, using

t-expansion [i] based on digital (32, 145, 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]

(34, 145, 128)-Net over F₉ — Digital

Digital (34, 145, 128)-net over F₉, using

t-expansion [i] based on digital (33, 145, 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]

(34, 145, 806)-Net in Base 9 — Upper bound on s

There is no (34, 145, 807)-net in base 9, because

1 times m-reduction [i] would yield (34, 144, 807)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 260230 276262 581978 747689 462795 438979 921553 402997 721479 227364 912467 686088 958531 355593 522642 569382 008132 299318 226986 208060 223106 407567 043081 > 9¹⁴⁴ [i]