MinT - Best Known (172, 172+88, s)-Nets in Base 4

Best Known (172, 172+88, s)-Nets in Base 4

(172, 172+88, 450)-Net over F₄ — Constructive and digital

Digital (172, 260, 450)-net over F₄, using

t-expansion [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]

(172, 172+88, 657)-Net over F₄ — Digital

Digital (172, 260, 657)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+88, 20733)-Net in Base 4 — Upper bound on s

There is no (172, 260, 20734)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 436155 988366 852755 592297 664200 136958 345270 091517 334760 188534 868433 287699 149895 670993 133855 287547 810612 016123 511345 155123 601070 973509 974839 467914 834728 083667 > 4²⁶⁰ [i]