MinT - Best Known (46−31, 46, s)-Nets in Base 81

Best Known (46−31, 46, s)-Nets in Base 81

(46−31, 46, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 46, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 46, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(46−31, 46, 298)-Net over F₈₁ — Digital

Digital (15, 46, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 46, 298)-net over F₈₁, using
- net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
    - a curve from the manYPoints database [i]

(46−31, 46, 42663)-Net in Base 81 — Upper bound on s

There is no (15, 46, 42664)-net in base 81, because

1 times m-reduction [i] would yield (15, 45, 42664)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 76 185284 078354 262886 995392 077122 457786 279093 304293 490249 148066 854187 572661 483948 156801 > 81⁴⁵ [i]