MinT - Best Known (93, 93+57, s)-Nets in Base 4

Best Known (93, 93+57, s)-Nets in Base 4

(93, 93+57, 130)-Net over F₄ — Constructive and digital

Digital (93, 150, 130)-net over F₄, using

24 times m-reduction [i] based on digital (93, 174, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 87, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(93, 93+57, 272)-Net over F₄ — Digital

Digital (93, 150, 272)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+57, 5998)-Net in Base 4 — Upper bound on s

There is no (93, 150, 5999)-net in base 4, because

1 times m-reduction [i] would yield (93, 149, 5999)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 510025 210946 206172 115425 729831 783451 732083 741613 115558 400221 783198 701276 717865 002230 315482 > 4¹⁴⁹ [i]