MinT - Best Known (49−35, 49, s)-Nets in Base 81

Best Known (49−35, 49, s)-Nets in Base 81

(49−35, 49, 224)-Net over F₈₁ — Constructive and digital

Digital (14, 49, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 49, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(49−35, 49, 298)-Net over F₈₁ — Digital

Digital (14, 49, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 49, 298)-net over F₈₁, using
- net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
    - a curve from the manYPoints database [i]

(49−35, 49, 21946)-Net in Base 81 — Upper bound on s

There is no (14, 49, 21947)-net in base 81, because

1 times m-reduction [i] would yield (14, 48, 21947)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 40 513616 893483 511221 287018 936947 202085 310223 483510 873844 823322 857066 191850 054968 011377 099121 > 81⁴⁸ [i]