MinT - Best Known (172, 172+87, s)-Nets in Base 4

Best Known (172, 172+87, s)-Nets in Base 4

(172, 172+87, 450)-Net over F₄ — Constructive and digital

Digital (172, 259, 450)-net over F₄, using

t-expansion [i] based on digital (170, 259, 450)-net over F₄, using
- 1 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]

(172, 172+87, 672)-Net over F₄ — Digital

Digital (172, 259, 672)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+87, 23016)-Net in Base 4 — Upper bound on s

There is no (172, 259, 23017)-net in base 4, because

1 times m-reduction [i] would yield (172, 258, 23017)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214679 606439 030170 692227 115165 644159 573555 759821 391429 989230 301767 769643 677671 766171 026544 713305 858218 231885 745711 251340 149993 807572 317244 933711 797075 086464 > 4²⁵⁸ [i]