MinT - Best Known (71−51, 71, s)-Nets in Base 81

Best Known (71−51, 71, s)-Nets in Base 81

(71−51, 71, 370)-Net over F₈₁ — Constructive and digital

Digital (20, 71, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 71, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(71−51, 71, 28061)-Net in Base 81 — Upper bound on s

There is no (20, 71, 28062)-net in base 81, because

1 times m-reduction [i] would yield (20, 70, 28062)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 39 294505 767906 959023 043293 613054 881630 162148 932266 975050 166456 462960 257182 894407 776282 829664 413582 053329 167964 053165 577452 223044 284001 > 81⁷⁰ [i]