MinT - Best Known (110−49, 110, s)-Nets in Base 4

Best Known (110−49, 110, s)-Nets in Base 4

(110−49, 110, 130)-Net over F₄ — Constructive and digital

Digital (61, 110, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 55, 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]

(110−49, 110, 1753)-Net in Base 4 — Upper bound on s

There is no (61, 110, 1754)-net in base 4, because

1 times m-reduction [i] would yield (61, 109, 1754)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 426255 422394 246727 480343 871753 761434 262862 418169 404657 348593 011029 > 4¹⁰⁹ [i]