MinT - Best Known (254−80, 254, s)-Nets in Base 4

Best Known (254−80, 254, s)-Nets in Base 4

(254−80, 254, 450)-Net over F₄ — Constructive and digital

Digital (174, 254, 450)-net over F₄, using

t-expansion [i] based on digital (170, 254, 450)-net over F₄, using
- 6 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]

(254−80, 254, 840)-Net over F₄ — Digital

Digital (174, 254, 840)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−80, 254, 34941)-Net in Base 4 — Upper bound on s

There is no (174, 254, 34942)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 838 350058 005742 685628 579562 479315 090759 116448 393523 576182 012279 537414 706855 763512 983364 914094 556480 581509 747029 648525 171662 133019 255044 619451 996524 636625 > 4²⁵⁴ [i]