MinT - Best Known (94−34, 94, s)-Nets in Base 4

Best Known (94−34, 94, s)-Nets in Base 4

(94−34, 94, 130)-Net over F₄ — Constructive and digital

Digital (60, 94, 130)-net over F₄, using

14 times m-reduction [i] based on digital (60, 108, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 54, 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]

(94−34, 94, 220)-Net over F₄ — Digital

Digital (60, 94, 220)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−34, 94, 5089)-Net in Base 4 — Upper bound on s

There is no (60, 94, 5090)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 392 619114 311192 371742 223711 487619 216867 867841 668606 688550 > 4⁹⁴ [i]