MinT - Best Known (223−73, 223, s)-Nets in Base 4

Best Known (223−73, 223, s)-Nets in Base 4

(223−73, 223, 240)-Net over F₄ — Constructive and digital

Digital (150, 223, 240)-net over F₄, using

4¹ times duplication [i] based on digital (149, 222, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 74, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(223−73, 223, 647)-Net over F₄ — Digital

Digital (150, 223, 647)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−73, 223, 24535)-Net in Base 4 — Upper bound on s

There is no (150, 223, 24536)-net in base 4, because

1 times m-reduction [i] would yield (150, 222, 24536)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 450981 389044 871516 476977 612373 293602 449232 048127 990650 514128 369977 893840 455784 484310 685572 188441 779179 615265 713540 667868 278000 945634 > 4²²² [i]