MinT - Best Known (146−60, 146, s)-Nets in Base 4

Best Known (146−60, 146, s)-Nets in Base 4

(146−60, 146, 130)-Net over F₄ — Constructive and digital

Digital (86, 146, 130)-net over F₄, using

14 times m-reduction [i] based on digital (86, 160, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 80, 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]

(146−60, 146, 204)-Net over F₄ — Digital

Digital (86, 146, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−60, 146, 3392)-Net in Base 4 — Upper bound on s

There is no (86, 146, 3393)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7961 167695 913161 840929 043995 819656 290097 959643 637083 987350 597774 850860 012175 711854 510112 > 4¹⁴⁶ [i]