MinT - Best Known (90−35, 90, s)-Nets in Base 4

Best Known (90−35, 90, s)-Nets in Base 4

(90−35, 90, 130)-Net over F₄ — Constructive and digital

Digital (55, 90, 130)-net over F₄, using

8 times m-reduction [i] based on digital (55, 98, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 49, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(90−35, 90, 166)-Net over F₄ — Digital

Digital (55, 90, 166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−35, 90, 3380)-Net in Base 4 — Upper bound on s

There is no (55, 90, 3381)-net in base 4, because

1 times m-reduction [i] would yield (55, 89, 3381)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 383263 804755 879598 902403 883562 955268 848780 595954 377168 > 4⁸⁹ [i]