MinT - Best Known (48, 48+43, s)-Nets in Base 3

Best Known (48, 48+43, s)-Nets in Base 3

(48, 48+43, 48)-Net over F₃ — Constructive and digital

Digital (48, 91, 48)-net over F₃, using

t-expansion [i] based on digital (45, 91, 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]

(48, 48+43, 62)-Net over F₃ — Digital

Digital (48, 91, 62)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+43, 460)-Net in Base 3 — Upper bound on s

There is no (48, 91, 461)-net in base 3, because

1 times m-reduction [i] would yield (48, 90, 461)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 730528 594830 379695 452252 450683 747651 051627 > 3⁹⁰ [i]