MinT - Best Known (75, 75+57, s)-Nets in Base 4

Best Known (75, 75+57, s)-Nets in Base 4

(75, 75+57, 130)-Net over F₄ — Constructive and digital

Digital (75, 132, 130)-net over F₄, using

6 times m-reduction [i] based on digital (75, 138, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 69, 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]

(75, 75+57, 160)-Net over F₄ — Digital

Digital (75, 132, 160)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+57, 2447)-Net in Base 4 — Upper bound on s

There is no (75, 132, 2448)-net in base 4, because

1 times m-reduction [i] would yield (75, 131, 2448)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 489852 453065 708953 568318 512907 559859 551495 209004 763282 192146 031031 675245 629000 > 4¹³¹ [i]