MinT - Best Known (56, 56+39, s)-Nets in Base 4

Best Known (56, 56+39, s)-Nets in Base 4

(56, 56+39, 130)-Net over F₄ — Constructive and digital

Digital (56, 95, 130)-net over F₄, using

5 times m-reduction [i] based on digital (56, 100, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 50, 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]

(56, 56+39, 145)-Net over F₄ — Digital

Digital (56, 95, 145)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+39, 2500)-Net in Base 4 — Upper bound on s

There is no (56, 95, 2501)-net in base 4, because

1 times m-reduction [i] would yield (56, 94, 2501)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 393 265853 754284 745458 578637 399590 778805 593174 818128 548944 > 4⁹⁴ [i]