MinT - Best Known (201, 201+51, s)-Nets in Base 4

Best Known (201, 201+51, s)-Nets in Base 4

(201, 201+51, 1539)-Net over F₄ — Constructive and digital

Digital (201, 252, 1539)-net over F₄, using

t-expansion [i] based on digital (200, 252, 1539)-net over F₄, using
- 6 times m-reduction [i] based on digital (200, 258, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 86, 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]

(201, 201+51, 7054)-Net over F₄ — Digital

Digital (201, 252, 7054)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(201, 201+51, 3759971)-Net in Base 4 — Upper bound on s

There is no (201, 252, 3759972)-net in base 4, because

1 times m-reduction [i] would yield (201, 251, 3759972)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 093618 226915 810582 751338 205898 317330 236913 419566 074057 409480 728709 592419 033889 692912 113383 465772 616019 370454 231779 116907 258371 317277 163934 391673 487108 > 4²⁵¹ [i]