MinT - Best Known (28, 28+47, s)-Nets in Base 81

Best Known (28, 28+47, s)-Nets in Base 81

(28, 28+47, 370)-Net over F₈₁ — Constructive and digital

Digital (28, 75, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 75, 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]

(28, 28+47, 500)-Net over F₈₁ — Digital

Digital (28, 75, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 75, 500)-net over F₈₁, using
- net from sequence [i] based on digital (26, 499)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 26 and N(F) ≥ 500, using
    - a curve from the manYPoints database [i]

(28, 28+47, 162809)-Net in Base 81 — Upper bound on s

There is no (28, 75, 162810)-net in base 81, because

1 times m-reduction [i] would yield (28, 74, 162810)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 1690 178247 986066 540491 982773 183183 485549 500769 561664 856243 149159 547953 861530 293181 368871 993630 527031 569894 329723 265745 620346 210334 366800 146401 > 81⁷⁴ [i]