MinT - Best Known (55, 55+132, s)-Nets in Base 4

Best Known (55, 55+132, s)-Nets in Base 4

(55, 55+132, 66)-Net over F₄ — Constructive and digital

Digital (55, 187, 66)-net over F₄, using

t-expansion [i] based on digital (49, 187, 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]

(55, 55+132, 91)-Net over F₄ — Digital

Digital (55, 187, 91)-net over F₄, using

t-expansion [i] based on digital (50, 187, 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]

(55, 55+132, 378)-Net in Base 4 — Upper bound on s

There is no (55, 187, 379)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42818 877148 984062 557969 079532 192607 647906 172980 765496 380684 107422 719534 050921 451458 744669 232785 593449 163962 268107 > 4¹⁸⁷ [i]