MinT - Best Known (26−11, 26, s)-Nets in Base 4

Best Known (26−11, 26, s)-Nets in Base 4

(26−11, 26, 66)-Net over F₄ — Constructive and digital

Digital (15, 26, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 13, 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]

(26−11, 26, 885)-Net in Base 4 — Upper bound on s

There is no (15, 26, 886)-net in base 4, because

1 times m-reduction [i] would yield (15, 25, 886)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1128 617315 097235 > 4²⁵ [i]