MinT - Best Known (87−35, 87, s)-Nets in Base 4

Best Known (87−35, 87, s)-Nets in Base 4

(87−35, 87, 130)-Net over F₄ — Constructive and digital

Digital (52, 87, 130)-net over F₄, using

5 times m-reduction [i] based on digital (52, 92, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 46, 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]

(87−35, 87, 145)-Net over F₄ — Digital

Digital (52, 87, 145)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−35, 87, 2644)-Net in Base 4 — Upper bound on s

There is no (52, 87, 2645)-net in base 4, because

1 times m-reduction [i] would yield (52, 86, 2645)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6014 554757 531995 086152 910705 008073 781214 163045 479632 > 4⁸⁶ [i]