MinT - Best Known (58, 58+24, s)-Nets in Base 4

Best Known (58, 58+24, s)-Nets in Base 4

(58, 58+24, 312)-Net over F₄ — Constructive and digital

Digital (58, 82, 312)-net over F₄, using

4¹ times duplication [i] based on digital (57, 81, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 27, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(58, 58+24, 452)-Net over F₄ — Digital

Digital (58, 82, 452)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+24, 22915)-Net in Base 4 — Upper bound on s

There is no (58, 82, 22916)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 385331 917319 606530 984619 977822 603166 183002 677920 > 4⁸² [i]