MinT - Best Known (95, 130, s)-Nets in Base 4

Best Known (95, 130, s)-Nets in Base 4

(95, 130, 531)-Net over F₄ — Constructive and digital

Digital (95, 130, 531)-net over F₄, using

2 times m-reduction [i] based on digital (95, 132, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 44, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(95, 130, 921)-Net over F₄ — Digital

Digital (95, 130, 921)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(95, 130, 88578)-Net in Base 4 — Upper bound on s

There is no (95, 130, 88579)-net in base 4, because

1 times m-reduction [i] would yield (95, 129, 88579)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 463185 451288 212678 745932 430513 400069 137728 346157 269297 434902 858921 379170 714560 > 4¹²⁹ [i]