MinT - Best Known (63−29, 63, s)-Nets in Base 4

Best Known (63−29, 63, s)-Nets in Base 4

(63−29, 63, 66)-Net over F₄ — Constructive and digital

Digital (34, 63, 66)-net over F₄, using

1 times m-reduction [i] based on digital (34, 64, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 32, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]

(63−29, 63, 74)-Net over F₄ — Digital

Digital (34, 63, 74)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−29, 63, 923)-Net in Base 4 — Upper bound on s

There is no (34, 63, 924)-net in base 4, because

1 times m-reduction [i] would yield (34, 62, 924)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 21 448639 650041 799314 841121 352110 503004 > 4⁶² [i]