MinT - Best Known (48, 80, s)-Nets in Base 4

Best Known (48, 80, s)-Nets in Base 4

(48, 80, 130)-Net over F₄ — Constructive and digital

Digital (48, 80, 130)-net over F₄, using

4 times m-reduction [i] based on digital (48, 84, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 42, 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]

(48, 80, 138)-Net over F₄ — Digital

Digital (48, 80, 138)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 80, 2308)-Net in Base 4 — Upper bound on s

There is no (48, 80, 2309)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 467354 129570 187536 314745 477110 598826 318486 738864 > 4⁸⁰ [i]