MinT - Best Known (76, 112, s)-Nets in Base 4

Best Known (76, 112, s)-Nets in Base 4

(76, 112, 240)-Net over F₄ — Constructive and digital

Digital (76, 112, 240)-net over F₄, using

4¹ times duplication [i] based on digital (75, 111, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 37, 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]

(76, 112, 394)-Net over F₄ — Digital

Digital (76, 112, 394)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 112, 14018)-Net in Base 4 — Upper bound on s

There is no (76, 112, 14019)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 26 966607 534737 734907 118643 437241 441821 565102 427351 355436 032887 205364 > 4¹¹² [i]