MinT - Best Known (60, 60+25, s)-Nets in Base 4

Best Known (60, 60+25, s)-Nets in Base 4

(60, 60+25, 312)-Net over F₄ — Constructive and digital

Digital (60, 85, 312)-net over F₄, using

4¹ times duplication [i] based on digital (59, 84, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 28, 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]

(60, 60+25, 455)-Net over F₄ — Digital

Digital (60, 85, 455)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+25, 28874)-Net in Base 4 — Upper bound on s

There is no (60, 85, 28875)-net in base 4, because

1 times m-reduction [i] would yield (60, 84, 28875)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 374 193399 094036 410731 820823 602006 856652 385056 062576 > 4⁸⁴ [i]