MinT - Best Known (106−47, 106, s)-Nets in Base 4

Best Known (106−47, 106, s)-Nets in Base 4

(106−47, 106, 130)-Net over F₄ — Constructive and digital

Digital (59, 106, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 53, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(106−47, 106, 1742)-Net in Base 4 — Upper bound on s

There is no (59, 106, 1743)-net in base 4, because

1 times m-reduction [i] would yield (59, 105, 1743)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1648 579915 996316 778045 348185 398366 818012 137163 294218 473151 458000 > 4¹⁰⁵ [i]