MinT - Best Known (85, 85+63, s)-Nets in Base 4

Best Known (85, 85+63, s)-Nets in Base 4

(85, 85+63, 130)-Net over F₄ — Constructive and digital

Digital (85, 148, 130)-net over F₄, using

10 times m-reduction [i] based on digital (85, 158, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 79, 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]

(85, 85+63, 184)-Net over F₄ — Digital

Digital (85, 148, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+63, 2938)-Net in Base 4 — Upper bound on s

There is no (85, 148, 2939)-net in base 4, because

1 times m-reduction [i] would yield (85, 147, 2939)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31996 248590 355882 098410 150235 678556 091532 539929 643888 145291 903851 665569 907363 358119 125440 > 4¹⁴⁷ [i]