MinT - Best Known (244−134, 244, s)-Nets in Base 4

Best Known (244−134, 244, s)-Nets in Base 4

(244−134, 244, 130)-Net over F₄ — Constructive and digital

Digital (110, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(244−134, 244, 165)-Net over F₄ — Digital

Digital (110, 244, 165)-net over F₄, using

t-expansion [i] based on digital (109, 244, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(244−134, 244, 1284)-Net in Base 4 — Upper bound on s

There is no (110, 244, 1285)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 812 613080 007826 093860 951923 017141 599550 582078 995955 037027 321384 413186 859993 381252 824889 413604 395424 628055 064990 577554 928077 333521 481788 843419 756400 > 4²⁴⁴ [i]