MinT - Best Known (55, 55+122, s)-Nets in Base 4

Best Known (55, 55+122, s)-Nets in Base 4

(55, 55+122, 66)-Net over F₄ — Constructive and digital

Digital (55, 177, 66)-net over F₄, using

t-expansion [i] based on digital (49, 177, 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+122, 91)-Net over F₄ — Digital

Digital (55, 177, 91)-net over F₄, using

t-expansion [i] based on digital (50, 177, 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+122, 390)-Net in Base 4 — Upper bound on s

There is no (55, 177, 391)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40227 132723 144180 354085 279026 622428 404092 321612 022508 888533 675422 693895 129755 597231 032022 226722 729355 263840 > 4¹⁷⁷ [i]