MinT - Best Known (61, 61+45, s)-Nets in Base 4

Best Known (61, 61+45, s)-Nets in Base 4

(61, 61+45, 130)-Net over F₄ — Constructive and digital

Digital (61, 106, 130)-net over F₄, using

4 times m-reduction [i] based on 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]

(61, 61+45, 141)-Net over F₄ — Digital

Digital (61, 106, 141)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+45, 2237)-Net in Base 4 — Upper bound on s

There is no (61, 106, 2238)-net in base 4, because

1 times m-reduction [i] would yield (61, 105, 2238)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1653 581525 003042 750954 390060 391791 456036 709829 511160 844912 526668 > 4¹⁰⁵ [i]