MinT - Best Known (124−49, 124, s)-Nets in Base 4

Best Known (124−49, 124, s)-Nets in Base 4

(124−49, 124, 130)-Net over F₄ — Constructive and digital

Digital (75, 124, 130)-net over F₄, using

14 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]

(124−49, 124, 204)-Net over F₄ — Digital

Digital (75, 124, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−49, 124, 3959)-Net in Base 4 — Upper bound on s

There is no (75, 124, 3960)-net in base 4, because

1 times m-reduction [i] would yield (75, 123, 3960)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 113 238055 008395 691330 151617 665198 177417 697582 130196 248345 847147 606778 469324 > 4¹²³ [i]