MinT - Best Known (50, 50+35, s)-Nets in Base 4

Best Known (50, 50+35, s)-Nets in Base 4

(50, 50+35, 130)-Net over F₄ — Constructive and digital

Digital (50, 85, 130)-net over F₄, using

3 times m-reduction [i] based on digital (50, 88, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 44, 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]

(50, 50+35, 132)-Net over F₄ — Digital

Digital (50, 85, 132)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+35, 2244)-Net in Base 4 — Upper bound on s

There is no (50, 85, 2245)-net in base 4, because

1 times m-reduction [i] would yield (50, 84, 2245)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 376 161822 919235 212270 781412 059467 160027 320032 295552 > 4⁸⁴ [i]