MinT - Best Known (210−98, 210, s)-Nets in Base 4

Best Known (210−98, 210, s)-Nets in Base 4

(210−98, 210, 130)-Net over F₄ — Constructive and digital

Digital (112, 210, 130)-net over F₄, using

t-expansion [i] based on digital (105, 210, 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]

(210−98, 210, 186)-Net over F₄ — Digital

Digital (112, 210, 186)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−98, 210, 2383)-Net in Base 4 — Upper bound on s

There is no (112, 210, 2384)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 739215 053311 557577 223162 332488 836271 448404 492894 003223 467506 945574 854161 899880 312564 102844 691740 057577 302403 036591 789157 977284 > 4²¹⁰ [i]