MinT - Best Known (231−47, 231, s)-Nets in Base 4

Best Known (231−47, 231, s)-Nets in Base 4

(231−47, 231, 1539)-Net over F₄ — Constructive and digital

Digital (184, 231, 1539)-net over F₄, using

3 times m-reduction [i] based on digital (184, 234, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 78, 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]

(231−47, 231, 6354)-Net over F₄ — Digital

Digital (184, 231, 6354)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−47, 231, 3295584)-Net in Base 4 — Upper bound on s

There is no (184, 231, 3295585)-net in base 4, because

1 times m-reduction [i] would yield (184, 230, 3295585)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 977137 613542 460908 272193 096529 256667 917580 437441 199376 997555 804061 770264 532181 517170 930000 045385 892664 415009 618561 110306 344814 334299 762144 > 4²³⁰ [i]