MinT - Best Known (57, 57+102, s)-Nets in Base 4

Best Known (57, 57+102, s)-Nets in Base 4

(57, 57+102, 66)-Net over F₄ — Constructive and digital

Digital (57, 159, 66)-net over F₄, using

t-expansion [i] based on digital (49, 159, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(57, 57+102, 91)-Net over F₄ — Digital

Digital (57, 159, 91)-net over F₄, using

t-expansion [i] based on digital (50, 159, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(57, 57+102, 457)-Net in Base 4 — Upper bound on s

There is no (57, 159, 458)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 540158 652428 687243 060581 015087 886585 926184 759559 553882 843388 598940 746359 315199 347586 255802 447600 > 4¹⁵⁹ [i]