MinT - Best Known (132−49, 132, s)-Nets in Base 4

Best Known (132−49, 132, s)-Nets in Base 4

(132−49, 132, 130)-Net over F₄ — Constructive and digital

Digital (83, 132, 130)-net over F₄, using

22 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]

(132−49, 132, 264)-Net over F₄ — Digital

Digital (83, 132, 264)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−49, 132, 6297)-Net in Base 4 — Upper bound on s

There is no (83, 132, 6298)-net in base 4, because

1 times m-reduction [i] would yield (83, 131, 6298)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 434507 886064 883511 240887 736488 856508 247463 311665 636608 116797 857480 337432 050081 > 4¹³¹ [i]