MinT - Best Known (102−45, 102, s)-Nets in Base 4

Best Known (102−45, 102, s)-Nets in Base 4

(102−45, 102, 130)-Net over F₄ — Constructive and digital

Digital (57, 102, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 51, 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]

(102−45, 102, 1735)-Net in Base 4 — Upper bound on s

There is no (57, 102, 1736)-net in base 4, because

1 times m-reduction [i] would yield (57, 101, 1736)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 505259 335397 838067 751746 292482 055851 442329 573770 344064 322876 > 4¹⁰¹ [i]