MinT - Best Known (63−27, 63, s)-Nets in Base 4

Best Known (63−27, 63, s)-Nets in Base 4

(63−27, 63, 90)-Net over F₄ — Constructive and digital

Digital (36, 63, 90)-net over F₄, using

1 times m-reduction [i] based on digital (36, 64, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 32, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(63−27, 63, 93)-Net over F₄ — Digital

Digital (36, 63, 93)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−27, 63, 1394)-Net in Base 4 — Upper bound on s

There is no (36, 63, 1395)-net in base 4, because

1 times m-reduction [i] would yield (36, 62, 1395)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 21 345622 478545 453186 316758 169426 603560 > 4⁶² [i]