MinT - Best Known (245−67, 245, s)-Nets in Base 4

Best Known (245−67, 245, s)-Nets in Base 4

(245−67, 245, 531)-Net over F₄ — Constructive and digital

Digital (178, 245, 531)-net over F₄, using

t-expansion [i] based on digital (177, 245, 531)-net over F₄, using
- 10 times m-reduction [i] based on digital (177, 255, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 85, 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]

(245−67, 245, 1471)-Net over F₄ — Digital

Digital (178, 245, 1471)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−67, 245, 124089)-Net in Base 4 — Upper bound on s

There is no (178, 245, 124090)-net in base 4, because

1 times m-reduction [i] would yield (178, 244, 124090)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799 369110 995688 722939 795296 717870 944858 965356 019839 790591 122288 067541 003742 981797 223798 157700 189358 945803 628983 455289 314757 576295 577971 127570 671105 > 4²⁴⁴ [i]