MinT - Best Known (230−74, 230, s)-Nets in Base 4

Best Known (230−74, 230, s)-Nets in Base 4

(230−74, 230, 450)-Net over F₄ — Constructive and digital

Digital (156, 230, 450)-net over F₄, using

2 times m-reduction [i] based on digital (156, 232, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 116, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(230−74, 230, 709)-Net over F₄ — Digital

Digital (156, 230, 709)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−74, 230, 26967)-Net in Base 4 — Upper bound on s

There is no (156, 230, 26968)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 979950 913500 619651 935586 386498 268785 715217 659416 926737 813838 162061 670797 371545 225268 513472 341640 530142 172072 596624 359968 071507 071905 385750 > 4²³⁰ [i]