MinT - Best Known (28, 28+53, s)-Nets in Base 81

Best Known (28, 28+53, s)-Nets in Base 81

(28, 28+53, 370)-Net over F₈₁ — Constructive and digital

Digital (28, 81, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 81, 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+53, 500)-Net over F₈₁ — Digital

Digital (28, 81, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 81, 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+53, 98267)-Net in Base 81 — Upper bound on s

There is no (28, 81, 98268)-net in base 81, because

1 times m-reduction [i] would yield (28, 80, 98268)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 477 429473 817439 123857 840323 495734 651694 241202 608624 341674 329398 362107 430192 149810 302889 665861 715772 242611 448045 688319 383445 122022 818608 104383 713484 077441 > 81⁸⁰ [i]