MinT - Best Known (28, 28+49, s)-Nets in Base 81

Best Known (28, 28+49, s)-Nets in Base 81

(28, 28+49, 370)-Net over F₈₁ — Constructive and digital

Digital (28, 77, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 77, 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]

(28, 28+49, 500)-Net over F₈₁ — Digital

Digital (28, 77, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 77, 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]

(28, 28+49, 135447)-Net in Base 81 — Upper bound on s

There is no (28, 77, 135448)-net in base 81, because

1 times m-reduction [i] would yield (28, 76, 135448)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11 089304 870241 797798 638138 812120 515580 784782 278966 629331 609239 360878 513293 927464 740003 827983 820117 706921 982188 755066 066666 338720 397569 979888 706561 > 81⁷⁶ [i]