MinT - Best Known (71−43, 71, s)-Nets in Base 81

Best Known (71−43, 71, s)-Nets in Base 81

(71−43, 71, 370)-Net over F₈₁ — Constructive and digital

Digital (28, 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]

(71−43, 71, 500)-Net over F₈₁ — Digital

Digital (28, 71, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 71, 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]

(71−43, 71, 249460)-Net in Base 81 — Upper bound on s

There is no (28, 71, 249461)-net in base 81, because

1 times m-reduction [i] would yield (28, 70, 249461)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 39 262399 224149 435640 088242 150004 196574 529472 949249 012914 525965 185323 347033 175534 499789 430712 556296 697315 279985 226316 574310 441484 758481 > 81⁷⁰ [i]