MinT - Best Known (86, 86+57, s)-Nets in Base 4

Best Known (86, 86+57, s)-Nets in Base 4

(86, 86+57, 130)-Net over F₄ — Constructive and digital

Digital (86, 143, 130)-net over F₄, using

17 times m-reduction [i] based on digital (86, 160, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 80, 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]

(86, 86+57, 222)-Net over F₄ — Digital

Digital (86, 143, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+57, 4235)-Net in Base 4 — Upper bound on s

There is no (86, 143, 4236)-net in base 4, because

1 times m-reduction [i] would yield (86, 142, 4236)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 279386 647299 227251 025770 746891 524920 189799 035318 820303 219334 848022 549769 907152 308384 > 4¹⁴² [i]