MinT - Best Known (252−54, 252, s)-Nets in Base 4

Best Known (252−54, 252, s)-Nets in Base 4

(252−54, 252, 1539)-Net over F₄ — Constructive and digital

Digital (198, 252, 1539)-net over F₄, using

3 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]

(252−54, 252, 5030)-Net over F₄ — Digital

Digital (198, 252, 5030)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−54, 252, 1515325)-Net in Base 4 — Upper bound on s

There is no (198, 252, 1515326)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 375158 302858 571560 606369 866449 888009 215883 232417 055691 861078 775353 892160 283348 351334 947893 297001 223177 830759 818480 664902 197800 504739 190394 873104 234878 > 4²⁵² [i]