MinT - Best Known (123−58, 123, s)-Nets in Base 4

Best Known (123−58, 123, s)-Nets in Base 4

(123−58, 123, 76)-Net over F₄ — Constructive and digital

Digital (65, 123, 76)-net over F₄, using

1 times m-reduction [i] based on digital (65, 124, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 62, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(123−58, 123, 114)-Net over F₄ — Digital

Digital (65, 123, 114)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−58, 123, 1368)-Net in Base 4 — Upper bound on s

There is no (65, 123, 1369)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 114 857402 672305 191943 985313 925889 019268 219197 648259 783814 532066 826478 095744 > 4¹²³ [i]