MinT - Best Known (52, 52+53, s)-Nets in Base 3

Best Known (52, 52+53, s)-Nets in Base 3

(52, 52+53, 48)-Net over F₃ — Constructive and digital

Digital (52, 105, 48)-net over F₃, using

t-expansion [i] based on digital (45, 105, 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]

(52, 52+53, 64)-Net over F₃ — Digital

Digital (52, 105, 64)-net over F₃, using

t-expansion [i] based on digital (49, 105, 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]

(52, 52+53, 402)-Net in Base 3 — Upper bound on s

There is no (52, 105, 403)-net in base 3, because

1 times m-reduction [i] would yield (52, 104, 403)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 43 217371 326112 013069 055174 397512 163141 609998 800085 > 3¹⁰⁴ [i]