MinT - Best Known (223−62, 223, s)-Nets in Base 4

Best Known (223−62, 223, s)-Nets in Base 4

(223−62, 223, 531)-Net over F₄ — Constructive and digital

Digital (161, 223, 531)-net over F₄, using

8 times m-reduction [i] based on digital (161, 231, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 77, 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]

(223−62, 223, 1262)-Net over F₄ — Digital

Digital (161, 223, 1262)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−62, 223, 88661)-Net in Base 4 — Upper bound on s

There is no (161, 223, 88662)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 181 738191 297763 420205 193176 334107 367583 490449 191316 172832 930641 958151 229612 419585 271592 589410 407887 631694 289777 421682 201552 973672 552480 > 4²²³ [i]