MinT - Best Known (112, 208, s)-Nets in Base 4

Best Known (112, 208, s)-Nets in Base 4

(112, 208, 130)-Net over F₄ — Constructive and digital

Digital (112, 208, 130)-net over F₄, using

t-expansion [i] based on digital (105, 208, 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]

(112, 208, 191)-Net over F₄ — Digital

Digital (112, 208, 191)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 208, 2499)-Net in Base 4 — Upper bound on s

There is no (112, 208, 2500)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 171360 596337 539183 678213 755798 298394 403800 102143 770554 830476 197458 347795 554846 330358 715117 689933 732620 178221 771045 508623 066676 > 4²⁰⁸ [i]