MinT - Best Known (232−47, 232, s)-Nets in Base 4

Best Known (232−47, 232, s)-Nets in Base 4

(232−47, 232, 1539)-Net over F₄ — Constructive and digital

Digital (185, 232, 1539)-net over F₄, using

t-expansion [i] based on digital (184, 232, 1539)-net over F₄, using
- 2 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]

(232−47, 232, 6548)-Net over F₄ — Digital

Digital (185, 232, 6548)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−47, 232, 3500331)-Net in Base 4 — Upper bound on s

There is no (185, 232, 3500332)-net in base 4, because

1 times m-reduction [i] would yield (185, 231, 3500332)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 908585 520171 837493 092331 727281 953416 743444 931500 313499 501803 905033 260697 383495 387877 176843 956784 124236 808349 328742 873354 749683 315531 117972 > 4²³¹ [i]