MinT - Best Known (117, 117+56, s)-Nets in Base 4

Best Known (117, 117+56, s)-Nets in Base 4

(117, 117+56, 240)-Net over F₄ — Constructive and digital

Digital (117, 173, 240)-net over F₄, using

1 times m-reduction [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]

(117, 117+56, 542)-Net over F₄ — Digital

Digital (117, 173, 542)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+56, 19735)-Net in Base 4 — Upper bound on s

There is no (117, 173, 19736)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 405037 493500 136550 910759 321080 662177 217711 207835 607222 155501 910551 204819 209459 586883 838424 762029 585824 > 4¹⁷³ [i]