MinT - Best Known (174−56, 174, s)-Nets in Base 4

Best Known (174−56, 174, s)-Nets in Base 4

(174−56, 174, 240)-Net over F₄ — Constructive and digital

Digital (118, 174, 240)-net over F₄, using

t-expansion [i] based on digital (117, 174, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 58, 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]

(174−56, 174, 557)-Net over F₄ — Digital

Digital (118, 174, 557)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−56, 174, 20738)-Net in Base 4 — Upper bound on s

There is no (118, 174, 20739)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 573 704510 824726 572276 780765 606430 440073 543434 694463 540400 771353 987204 464662 525065 961063 297747 578128 272832 > 4¹⁷⁴ [i]