MinT - Best Known (174−73, 174, s)-Nets in Base 4

Best Known (174−73, 174, s)-Nets in Base 4

(174−73, 174, 130)-Net over F₄ — Constructive and digital

Digital (101, 174, 130)-net over F₄, using

16 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]

(174−73, 174, 222)-Net over F₄ — Digital

Digital (101, 174, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−73, 174, 3693)-Net in Base 4 — Upper bound on s

There is no (101, 174, 3694)-net in base 4, because

1 times m-reduction [i] would yield (101, 173, 3694)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 144 445459 583697 141845 084092 440372 967202 397809 679609 297971 113148 938908 137643 346857 236650 666389 099940 248865 > 4¹⁷³ [i]