MinT - Best Known (54, 54+48, s)-Nets in Base 4

Best Known (54, 54+48, s)-Nets in Base 4

(54, 54+48, 76)-Net over F₄ — Constructive and digital

Digital (54, 102, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 51, 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]

(54, 54+48, 99)-Net over F₄ — Digital

Digital (54, 102, 99)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+48, 1163)-Net in Base 4 — Upper bound on s

There is no (54, 102, 1164)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25 891710 918048 305406 398236 235332 824178 708185 986854 923080 404264 > 4¹⁰² [i]