MinT - Best Known (178−58, 178, s)-Nets in Base 4

Best Known (178−58, 178, s)-Nets in Base 4

(178−58, 178, 240)-Net over F₄ — Constructive and digital

Digital (120, 178, 240)-net over F₄, using

4¹ times duplication [i] based on digital (119, 177, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 59, 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]

(178−58, 178, 542)-Net over F₄ — Digital

Digital (120, 178, 542)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−58, 178, 19269)-Net in Base 4 — Upper bound on s

There is no (120, 178, 19270)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 146892 168349 235386 117710 411889 953156 665796 044821 130676 843446 277070 404534 937372 233404 290326 782469 800849 724424 > 4¹⁷⁸ [i]