MinT - Best Known (82−34, 82, s)-Nets in Base 4

Best Known (82−34, 82, s)-Nets in Base 4

(82−34, 82, 130)-Net over F₄ — Constructive and digital

Digital (48, 82, 130)-net over F₄, using

2 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]

(82−34, 82, 1904)-Net in Base 4 — Upper bound on s

There is no (48, 82, 1905)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 487676 793936 381543 902082 321479 311191 663886 448204 > 4⁸² [i]