MinT - Best Known (254−84, 254, s)-Nets in Base 4

Best Known (254−84, 254, s)-Nets in Base 4

(254−84, 254, 450)-Net over F₄ — Constructive and digital

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]

(254−84, 254, 699)-Net over F₄ — Digital

Digital (170, 254, 699)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−84, 254, 24048)-Net in Base 4 — Upper bound on s

There is no (170, 254, 24049)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 838 732442 494069 896286 563283 781630 280500 895862 038945 702670 052813 802133 234179 639327 434742 606558 667709 351276 677296 752524 897399 088371 268272 897572 524876 125000 > 4²⁵⁴ [i]