MinT - Best Known (26, 26+43, s)-Nets in Base 81

Best Known (26, 26+43, s)-Nets in Base 81

(26, 26+43, 370)-Net over F₈₁ — Constructive and digital

Digital (26, 69, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 69, 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]

(26, 26+43, 500)-Net over F₈₁ — Digital

Digital (26, 69, 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]

(26, 26+43, 164146)-Net in Base 81 — Upper bound on s

There is no (26, 69, 164147)-net in base 81, because

1 times m-reduction [i] would yield (26, 68, 164147)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5984 225253 141312 849695 105090 730830 054464 366292 226084 774667 155613 373072 501779 331277 331113 981478 466241 939078 657653 539241 876614 838961 > 81⁶⁸ [i]