MinT - Best Known (73, 128, s)-Nets in Base 4

Best Known (73, 128, s)-Nets in Base 4

(73, 128, 130)-Net over F₄ — Constructive and digital

Digital (73, 128, 130)-net over F₄, using

6 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, 128, 158)-Net over F₄ — Digital

Digital (73, 128, 158)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 128, 2450)-Net in Base 4 — Upper bound on s

There is no (73, 128, 2451)-net in base 4, because

1 times m-reduction [i] would yield (73, 127, 2451)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28972 542805 847389 261457 757399 220186 991586 683527 245590 154423 513308 102842 191808 > 4¹²⁷ [i]