MinT - Best Known (254−56, 254, s)-Nets in Base 4

Best Known (254−56, 254, s)-Nets in Base 4

(254−56, 254, 1539)-Net over F₄ — Constructive and digital

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]

(254−56, 254, 4317)-Net over F₄ — Digital

Digital (198, 254, 4317)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−56, 254, 1089980)-Net in Base 4 — Upper bound on s

There is no (198, 254, 1089981)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 837 990346 071484 650747 255908 967328 847449 516440 853055 398213 265036 000128 224527 149865 261466 604279 189769 843419 364608 052435 564033 883664 652905 804283 045870 717179 > 4²⁵⁴ [i]