MinT - Best Known (123−57, 123, s)-Nets in Base 4

Best Known (123−57, 123, s)-Nets in Base 4

(123−57, 123, 90)-Net over F₄ — Constructive and digital

Digital (66, 123, 90)-net over F₄, using

1 times m-reduction [i] based on digital (66, 124, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 62, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(123−57, 123, 121)-Net over F₄ — Digital

Digital (66, 123, 121)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−57, 123, 1559)-Net in Base 4 — Upper bound on s

There is no (66, 123, 1560)-net in base 4, because

1 times m-reduction [i] would yield (66, 122, 1560)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28 739090 475041 287878 680985 055251 973478 728229 595012 452120 694691 209709 677760 > 4¹²² [i]