MinT - Best Known (239−79, 239, s)-Nets in Base 4

Best Known (239−79, 239, s)-Nets in Base 4

(239−79, 239, 450)-Net over F₄ — Constructive and digital

Digital (160, 239, 450)-net over F₄, using

1 times m-reduction [i] based on digital (160, 240, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 120, 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]

(239−79, 239, 663)-Net over F₄ — Digital

Digital (160, 239, 663)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−79, 239, 24201)-Net in Base 4 — Upper bound on s

There is no (160, 239, 24202)-net in base 4, because

1 times m-reduction [i] would yield (160, 238, 24202)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195304 198387 808955 898491 890362 477747 729848 755377 471116 834450 001032 526772 318456 622833 399111 468953 968043 928098 084356 083378 195708 783903 528846 442832 > 4²³⁸ [i]