MinT - Best Known (87−41, 87, s)-Nets in Base 3

Best Known (87−41, 87, s)-Nets in Base 3

(87−41, 87, 48)-Net over F₃ — Constructive and digital

Digital (46, 87, 48)-net over F₃, using

t-expansion [i] based on digital (45, 87, 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]

(87−41, 87, 60)-Net over F₃ — Digital

Digital (46, 87, 60)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−41, 87, 448)-Net in Base 3 — Upper bound on s

There is no (46, 87, 449)-net in base 3, because

1 times m-reduction [i] would yield (46, 86, 449)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 110281 532418 431206 814239 573370 747506 862481 > 3⁸⁶ [i]