MinT - Best Known (27, 27+33, s)-Nets in Base 81

Best Known (27, 27+33, s)-Nets in Base 81

(27, 27+33, 370)-Net over F₈₁ — Constructive and digital

Digital (27, 60, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 60, 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]

(27, 27+33, 622)-Net over F₈₁ — Digital

Digital (27, 60, 622)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 27+33, 926794)-Net in Base 81 — Upper bound on s

There is no (27, 60, 926795)-net in base 81, because

1 times m-reduction [i] would yield (27, 59, 926795)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 39867 301742 296991 698271 895253 456129 895832 959771 912419 513688 711899 401214 333320 090248 650637 364206 361900 380995 577601 > 81⁵⁹ [i]