MinT - Best Known (151−93, 151, s)-Nets in Base 3

Best Known (151−93, 151, s)-Nets in Base 3

(151−93, 151, 48)-Net over F₃ — Constructive and digital

Digital (58, 151, 48)-net over F₃, using

t-expansion [i] based on digital (45, 151, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(151−93, 151, 64)-Net over F₃ — Digital

Digital (58, 151, 64)-net over F₃, using

t-expansion [i] based on digital (49, 151, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(151−93, 151, 280)-Net in Base 3 — Upper bound on s

There is no (58, 151, 281)-net in base 3, because

1 times m-reduction [i] would yield (58, 150, 281)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 392031 479295 733224 759618 979061 227610 979512 226075 216829 535542 403505 047145 > 3¹⁵⁰ [i]