MinT - Best Known (253−82, 253, s)-Nets in Base 4

Best Known (253−82, 253, s)-Nets in Base 4

(253−82, 253, 450)-Net over F₄ — Constructive and digital

Digital (171, 253, 450)-net over F₄, using

t-expansion [i] based on 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]

(253−82, 253, 751)-Net over F₄ — Digital

Digital (171, 253, 751)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−82, 253, 27888)-Net in Base 4 — Upper bound on s

There is no (171, 253, 27889)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209 780525 856130 752092 166725 797254 548152 648573 035705 678448 956948 984906 349153 092737 742399 147378 171692 566811 580370 751953 423620 545564 302683 887741 514258 425800 > 4²⁵³ [i]