MinT - Best Known (49, 49+31, s)-Nets in Base 4

Best Known (49, 49+31, s)-Nets in Base 4

(49, 49+31, 130)-Net over F₄ — Constructive and digital

Digital (49, 80, 130)-net over F₄, using

6 times m-reduction [i] based on digital (49, 86, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 43, 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]

(49, 49+31, 153)-Net over F₄ — Digital

Digital (49, 80, 153)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+31, 3161)-Net in Base 4 — Upper bound on s

There is no (49, 80, 3162)-net in base 4, because

1 times m-reduction [i] would yield (49, 79, 3162)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 366764 170367 775082 611561 617367 407825 043270 842440 > 4⁷⁹ [i]