MinT - Best Known (190−49, 190, s)-Nets in Base 3

Best Known (190−49, 190, s)-Nets in Base 3

(190−49, 190, 288)-Net over F₃ — Constructive and digital

Digital (141, 190, 288)-net over F₃, using

5 times m-reduction [i] based on digital (141, 195, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 65, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(190−49, 190, 722)-Net over F₃ — Digital

Digital (141, 190, 722)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−49, 190, 28009)-Net in Base 3 — Upper bound on s

There is no (141, 190, 28010)-net in base 3, because

1 times m-reduction [i] would yield (141, 189, 28010)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 500606 827223 429778 084846 114057 933723 217219 756897 120701 920862 103958 469249 846850 505852 158577 > 3¹⁸⁹ [i]