MinT - Best Known (198−57, 198, s)-Nets in Base 4

Best Known (198−57, 198, s)-Nets in Base 4

(198−57, 198, 531)-Net over F₄ — Constructive and digital

Digital (141, 198, 531)-net over F₄, using

3 times m-reduction [i] based on digital (141, 201, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 67, 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]

(198−57, 198, 980)-Net over F₄ — Digital

Digital (141, 198, 980)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−57, 198, 64811)-Net in Base 4 — Upper bound on s

There is no (141, 198, 64812)-net in base 4, because

1 times m-reduction [i] would yield (141, 197, 64812)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40354 214222 082106 814591 335723 881432 698818 667653 311780 512806 231507 692797 417017 016971 722341 708304 957538 672839 897387 455320 > 4¹⁹⁷ [i]