MinT - Best Known (55−48, 55, s)-Nets in Base 81

Best Known (55−48, 55, s)-Nets in Base 81

(55−48, 55, 172)-Net over F₈₁ — Constructive and digital

Digital (7, 55, 172)-net over F₈₁, using

net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
  - a function field by SÃ©mirat [i]

(55−48, 55, 190)-Net over F₈₁ — Digital

Digital (7, 55, 190)-net over F₈₁, using

t-expansion [i] based on digital (6, 55, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(55−48, 55, 2884)-Net in Base 81 — Upper bound on s

There is no (7, 55, 2885)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 927 821035 262644 296614 768286 498578 575951 334708 047028 326805 039512 603727 463351 454618 085401 967434 562166 051201 > 81⁵⁵ [i]