MinT - Best Known (26, 61, s)-Nets in Base 81

Best Known (26, 61, s)-Nets in Base 81

(26, 61, 370)-Net over F₈₁ — Constructive and digital

Digital (26, 61, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 61, 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, 61, 500)-Net over F₈₁ — Digital

Digital (26, 61, 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, 61, 488289)-Net in Base 81 — Upper bound on s

There is no (26, 61, 488290)-net in base 81, because

1 times m-reduction [i] would yield (26, 60, 488290)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 3 229301 165970 070404 186081 361338 752181 516430 392928 702464 486248 115415 818095 528703 892444 789723 971155 964251 232168 202401 > 81⁶⁰ [i]