MinT - Best Known (162−61, 162, s)-Nets in Base 4

Best Known (162−61, 162, s)-Nets in Base 4

(162−61, 162, 130)-Net over F₄ — Constructive and digital

Digital (101, 162, 130)-net over F₄, using

28 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 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]

(162−61, 162, 300)-Net over F₄ — Digital

Digital (101, 162, 300)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−61, 162, 6810)-Net in Base 4 — Upper bound on s

There is no (101, 162, 6811)-net in base 4, because

1 times m-reduction [i] would yield (101, 161, 6811)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 570811 865646 508925 447425 839290 697387 825119 634494 192015 534592 808296 293338 457229 678528 036151 386080 > 4¹⁶¹ [i]