MinT - Best Known (73, 73+49, s)-Nets in Base 4

Best Known (73, 73+49, s)-Nets in Base 4

(73, 73+49, 130)-Net over F₄ — Constructive and digital

Digital (73, 122, 130)-net over F₄, using

12 times m-reduction [i] based on digital (73, 134, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 67, 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]

(73, 73+49, 190)-Net over F₄ — Digital

Digital (73, 122, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+49, 3525)-Net in Base 4 — Upper bound on s

There is no (73, 122, 3526)-net in base 4, because

1 times m-reduction [i] would yield (73, 121, 3526)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 085050 770538 614656 975615 218295 553847 675263 795151 735746 175556 046144 379336 > 4¹²¹ [i]