MinT - Best Known (253−83, 253, s)-Nets in Base 4

Best Known (253−83, 253, s)-Nets in Base 4

(253−83, 253, 450)-Net over F₄ — Constructive and digital

Digital (170, 253, 450)-net over F₄, using

7 times m-reduction [i] based on digital (170, 260, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 130, 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]

(253−83, 253, 718)-Net over F₄ — Digital

Digital (170, 253, 718)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−83, 253, 26959)-Net in Base 4 — Upper bound on s

There is no (170, 253, 26960)-net in base 4, because

1 times m-reduction [i] would yield (170, 252, 26960)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 392487 271409 338976 717030 071840 120211 572813 559300 224924 681188 615420 350956 941593 319386 136917 477739 950504 342010 424018 376094 604009 235691 369692 252022 075714 > 4²⁵² [i]