MinT - Best Known (242−72, 242, s)-Nets in Base 4

Best Known (242−72, 242, s)-Nets in Base 4

(242−72, 242, 531)-Net over F₄ — Constructive and digital

Digital (170, 242, 531)-net over F₄, using

t-expansion [i] based on 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]

(242−72, 242, 1011)-Net over F₄ — Digital

Digital (170, 242, 1011)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−72, 242, 53034)-Net in Base 4 — Upper bound on s

There is no (170, 242, 53035)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 977545 035668 597550 097345 878687 544501 657743 945207 067509 097991 689413 979318 524310 115350 831327 562171 574439 531821 011247 862784 507714 298299 243256 678570 > 4²⁴² [i]