MinT - Best Known (90, 90+63, s)-Nets in Base 4

Best Known (90, 90+63, s)-Nets in Base 4

(90, 90+63, 130)-Net over F₄ — Constructive and digital

Digital (90, 153, 130)-net over F₄, using

15 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 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, 90+63, 211)-Net over F₄ — Digital

Digital (90, 153, 211)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+63, 3681)-Net in Base 4 — Upper bound on s

There is no (90, 153, 3682)-net in base 4, because

1 times m-reduction [i] would yield (90, 152, 3682)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 32 840298 179246 910812 664916 141876 031472 960311 377194 056375 432546 958489 945397 185713 260906 320400 > 4¹⁵² [i]