MinT - Best Known (258−83, 258, s)-Nets in Base 4

Best Known (258−83, 258, s)-Nets in Base 4

(258−83, 258, 450)-Net over F₄ — Constructive and digital

Digital (175, 258, 450)-net over F₄, using

t-expansion [i] based on digital (170, 258, 450)-net over F₄, using
- 2 times m-reduction [i] based on digital (170, 260, 450)-net over F₄, using
  - trace code for nets [i] based on digital (40, 130, 225)-net over F₁₆, using
    - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
        a function field by GarcÃa and Quoos [i]

(258−83, 258, 785)-Net over F₄ — Digital

Digital (175, 258, 785)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−83, 258, 31931)-Net in Base 4 — Upper bound on s

There is no (175, 258, 31932)-net in base 4, because

1 times m-reduction [i] would yield (175, 257, 31932)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53649 956477 670305 020179 116198 267758 396676 048693 703189 185947 239556 082789 405589 668086 705194 571190 424672 390561 023466 830243 404395 768749 999876 086439 973104 918125 > 4²⁵⁷ [i]