MinT - Best Known (25, 25+41, s)-Nets in Base 81

Best Known (25, 25+41, s)-Nets in Base 81

(25, 25+41, 370)-Net over F₈₁ — Constructive and digital

Digital (25, 66, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 66, 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]

(25, 25+41, 392)-Net over F₈₁ — Digital

Digital (25, 66, 392)-net over F₈₁, using

net from sequence [i] based on digital (25, 391)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 25 and N(F) ≥ 392, using
  - a curve from the manYPoints database [i]

(25, 25+41, 165488)-Net in Base 81 — Upper bound on s

There is no (25, 66, 165489)-net in base 81, because

1 times m-reduction [i] would yield (25, 65, 165489)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11260 805973 054732 860080 595686 427731 839504 920446 179794 288324 739313 010383 846614 280698 354782 377335 862880 012544 514765 974050 062401 > 81⁶⁵ [i]