MinT - Best Known (123−50, 123, s)-Nets in Base 4

Best Known (123−50, 123, s)-Nets in Base 4

(123−50, 123, 130)-Net over F₄ — Constructive and digital

Digital (73, 123, 130)-net over F₄, using

11 times m-reduction [i] based on digital (73, 134, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 67, 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]

(123−50, 123, 184)-Net over F₄ — Digital

Digital (73, 123, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−50, 123, 3088)-Net in Base 4 — Upper bound on s

There is no (73, 123, 3089)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 113 211209 005268 637193 121975 884606 486564 293649 865269 954158 430032 549052 215808 > 4¹²³ [i]