MinT - Best Known (53, 100, s)-Nets in Base 4

Best Known (53, 100, s)-Nets in Base 4

(53, 100, 76)-Net over F₄ — Constructive and digital

Digital (53, 100, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 50, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(53, 100, 98)-Net over F₄ — Digital

Digital (53, 100, 98)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 100, 1208)-Net in Base 4 — Upper bound on s

There is no (53, 100, 1209)-net in base 4, because

1 times m-reduction [i] would yield (53, 99, 1209)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 406687 607815 292397 021995 975974 692424 931126 656062 711949 137448 > 4⁹⁹ [i]