MinT - Best Known (254−55, 254, s)-Nets in Base 4

Best Known (254−55, 254, s)-Nets in Base 4

(254−55, 254, 1539)-Net over F₄ — Constructive and digital

Digital (199, 254, 1539)-net over F₄, using

t-expansion [i] based on digital (198, 254, 1539)-net over F₄, using
- 1 times m-reduction [i] based on digital (198, 255, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 85, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(254−55, 254, 4773)-Net over F₄ — Digital

Digital (199, 254, 4773)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−55, 254, 1595161)-Net in Base 4 — Upper bound on s

There is no (199, 254, 1595162)-net in base 4, because

1 times m-reduction [i] would yield (199, 253, 1595162)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209 499156 536517 296823 727862 330208 109604 343931 209548 877540 930983 266559 125433 844501 947035 582864 755492 075523 158297 613132 080677 958895 793715 637331 841906 298000 > 4²⁵³ [i]