MinT - Best Known (58, 58+25, s)-Nets in Base 4

Best Known (58, 58+25, s)-Nets in Base 4

(58, 58+25, 240)-Net over F₄ — Constructive and digital

Digital (58, 83, 240)-net over F₄, using

t-expansion [i] based on digital (57, 83, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (57, 84, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 28, 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]

(58, 58+25, 407)-Net over F₄ — Digital

Digital (58, 83, 407)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+25, 22915)-Net in Base 4 — Upper bound on s

There is no (58, 83, 22916)-net in base 4, because

1 times m-reduction [i] would yield (58, 82, 22916)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 385331 917319 606530 984619 977822 603166 183002 677920 > 4⁸² [i]