MinT - Best Known (184−60, 184, s)-Nets in Base 4

Best Known (184−60, 184, s)-Nets in Base 4

(184−60, 184, 240)-Net over F₄ — Constructive and digital

Digital (124, 184, 240)-net over F₄, using

4¹ times duplication [i] based on digital (123, 183, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 61, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(184−60, 184, 555)-Net over F₄ — Digital

Digital (124, 184, 555)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−60, 184, 19758)-Net in Base 4 — Upper bound on s

There is no (124, 184, 19759)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 601 261932 395834 079866 535818 272745 531469 270616 506348 884050 575725 583464 212202 623847 743499 490695 862966 401705 088298 > 4¹⁸⁴ [i]