MinT - Best Known (91−44, 91, s)-Nets in Base 3

Best Known (91−44, 91, s)-Nets in Base 3

(91−44, 91, 48)-Net over F₃ — Constructive and digital

Digital (47, 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]

(91−44, 91, 58)-Net over F₃ — Digital

Digital (47, 91, 58)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−44, 91, 404)-Net in Base 3 — Upper bound on s

There is no (47, 91, 405)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 315494 933292 903784 202581 660222 847021 973281 > 3⁹¹ [i]