MinT - Best Known (258−84, 258, s)-Nets in Base 4

Best Known (258−84, 258, s)-Nets in Base 4

(258−84, 258, 450)-Net over F₄ — Constructive and digital

Digital (174, 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]

(258−84, 258, 751)-Net over F₄ — Digital

Digital (174, 258, 751)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−84, 258, 27447)-Net in Base 4 — Upper bound on s

There is no (174, 258, 27448)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214667 062685 743556 385512 408407 544073 236244 144368 250684 450422 708731 855547 306055 992181 157913 568498 323940 947562 428603 473014 550626 951140 200309 190956 570082 204470 > 4²⁵⁸ [i]