MinT - Best Known (245−47, 245, s)-Nets in Base 4

Best Known (245−47, 245, s)-Nets in Base 4

(245−47, 245, 1539)-Net over F₄ — Constructive and digital

Digital (198, 245, 1539)-net over F₄, using

10 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]

(245−47, 245, 9677)-Net over F₄ — Digital

Digital (198, 245, 9677)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−47, 245, 7663112)-Net in Base 4 — Upper bound on s

There is no (198, 245, 7663113)-net in base 4, because

1 times m-reduction [i] would yield (198, 244, 7663113)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799 169764 909386 985793 217470 227172 879420 865531 202118 748999 430689 666297 316736 997027 441696 761261 195122 229843 619096 506031 982157 891110 873522 621181 436160 > 4²⁴⁴ [i]