MinT - Best Known (63, 63+25, s)-Nets in Base 4

Best Known (63, 63+25, s)-Nets in Base 4

(63, 63+25, 312)-Net over F₄ — Constructive and digital

Digital (63, 88, 312)-net over F₄, using

2 times m-reduction [i] based on digital (63, 90, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 30, 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]

(63, 63+25, 539)-Net over F₄ — Digital

Digital (63, 88, 539)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+25, 40838)-Net in Base 4 — Upper bound on s

There is no (63, 88, 40839)-net in base 4, because

1 times m-reduction [i] would yield (63, 87, 40839)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23945 909854 978372 782763 582972 768741 752077 303972 455120 > 4⁸⁷ [i]