MinT - Best Known (83, 83+51, s)-Nets in Base 4

Best Known (83, 83+51, s)-Nets in Base 4

(83, 83+51, 130)-Net over F₄ — Constructive and digital

Digital (83, 134, 130)-net over F₄, using

20 times m-reduction [i] based on digital (83, 154, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 77, 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]

(83, 83+51, 247)-Net over F₄ — Digital

Digital (83, 134, 247)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+51, 5393)-Net in Base 4 — Upper bound on s

There is no (83, 134, 5394)-net in base 4, because

1 times m-reduction [i] would yield (83, 133, 5394)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 119 110907 209147 619734 285907 651215 432682 792462 920911 376898 463519 802276 875156 276064 > 4¹³³ [i]