MinT - Best Known (242−73, 242, s)-Nets in Base 4

Best Known (242−73, 242, s)-Nets in Base 4

(242−73, 242, 531)-Net over F₄ — Constructive and digital

Digital (169, 242, 531)-net over F₄, using

1 times m-reduction [i] based on digital (169, 243, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 81, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(242−73, 242, 955)-Net over F₄ — Digital

Digital (169, 242, 955)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−73, 242, 51029)-Net in Base 4 — Upper bound on s

There is no (169, 242, 51030)-net in base 4, because

1 times m-reduction [i] would yield (169, 241, 51030)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 490622 829811 564929 609254 041094 027969 510226 953546 783032 601645 744502 571413 380149 325001 639260 599202 477175 824274 541156 584273 603064 815309 336471 099322 > 4²⁴¹ [i]