MinT - Best Known (224−44, 224, s)-Nets in Base 4

Best Known (224−44, 224, s)-Nets in Base 4

(224−44, 224, 1539)-Net over F₄ — Constructive and digital

Digital (180, 224, 1539)-net over F₄, using

4 times m-reduction [i] based on digital (180, 228, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 76, 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]

(224−44, 224, 7724)-Net over F₄ — Digital

Digital (180, 224, 7724)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−44, 224, 4071882)-Net in Base 4 — Upper bound on s

There is no (180, 224, 4071883)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 726 840721 097751 508683 511532 856111 965061 710381 291093 909255 873519 065588 929494 833453 907699 130283 172707 118585 366827 335742 970479 871599 399432 > 4²²⁴ [i]