MinT - Best Known (49, 49+32, s)-Nets in Base 4

Best Known (49, 49+32, s)-Nets in Base 4

(49, 49+32, 130)-Net over F₄ — Constructive and digital

Digital (49, 81, 130)-net over F₄, using

5 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+32, 145)-Net over F₄ — Digital

Digital (49, 81, 145)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+32, 2518)-Net in Base 4 — Upper bound on s

There is no (49, 81, 2519)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5 864258 953087 502521 471817 448162 828773 215082 291641 > 4⁸¹ [i]