MinT - Best Known (105, 105+45, s)-Nets in Base 4

Best Known (105, 105+45, s)-Nets in Base 4

(105, 105+45, 384)-Net over F₄ — Constructive and digital

Digital (105, 150, 384)-net over F₄, using

trace code for nets [i] based on digital (5, 50, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(105, 105+45, 656)-Net over F₄ — Digital

Digital (105, 150, 656)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+45, 36066)-Net in Base 4 — Upper bound on s

There is no (105, 150, 36067)-net in base 4, because

1 times m-reduction [i] would yield (105, 149, 36067)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 509381 998480 182152 763960 625939 655511 314352 997244 350422 996750 260775 176837 492994 059351 262760 > 4¹⁴⁹ [i]