MinT - Best Known (48−42, 48, s)-Nets in Base 81

Best Known (48−42, 48, s)-Nets in Base 81

(48−42, 48, 160)-Net over F₈₁ — Constructive and digital

Digital (6, 48, 160)-net over F₈₁, using

t-expansion [i] based on digital (5, 48, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(48−42, 48, 190)-Net over F₈₁ — Digital

Digital (6, 48, 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]

(48−42, 48, 2488)-Net in Base 81 — Upper bound on s

There is no (6, 48, 2489)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 40 791014 532170 331054 233171 767783 343522 029364 127894 928694 606917 397681 762899 549053 196401 301521 > 81⁴⁸ [i]