MinT - Best Known (27, 80, s)-Nets in Base 81

Best Known (27, 80, s)-Nets in Base 81

(27, 80, 370)-Net over F₈₁ — Constructive and digital

Digital (27, 80, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 80, 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]

(27, 80, 500)-Net over F₈₁ — Digital

Digital (27, 80, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 80, 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]

(27, 80, 82983)-Net in Base 81 — Upper bound on s

There is no (27, 80, 82984)-net in base 81, because

1 times m-reduction [i] would yield (27, 79, 82984)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5 892763 829719 451939 407815 277338 008110 337558 864002 012450 188138 766512 681264 979848 654807 927533 193354 188446 091844 812949 634208 394016 638327 654435 196758 206721 > 81⁷⁹ [i]