MinT - Best Known (6, 53, s)-Nets in Base 81

Best Known (6, 53, s)-Nets in Base 81

(6, 53, 160)-Net over F₈₁ — Constructive and digital

Digital (6, 53, 160)-net over F₈₁, using

t-expansion [i] based on digital (5, 53, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(6, 53, 190)-Net over F₈₁ — Digital

Digital (6, 53, 190)-net over F₈₁, using

net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
  - a curve from the manYPoints database [i]

(6, 53, 2422)-Net in Base 81 — Upper bound on s

There is no (6, 53, 2423)-net in base 81, because

1 times m-reduction [i] would yield (6, 52, 2423)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 1758 270918 584258 674797 614989 439695 028237 293312 251969 108336 903559 379887 168978 491720 754656 298673 437521 > 81⁵² [i]