MinT - Best Known (210−93, 210, s)-Nets in Base 4

Best Known (210−93, 210, s)-Nets in Base 4

(210−93, 210, 130)-Net over F₄ — Constructive and digital

Digital (117, 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]

(210−93, 210, 220)-Net over F₄ — Digital

Digital (117, 210, 220)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−93, 210, 3224)-Net in Base 4 — Upper bound on s

There is no (117, 210, 3225)-net in base 4, because

1 times m-reduction [i] would yield (117, 209, 3225)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 678188 992845 649171 800272 840235 676539 873120 369830 113729 402850 107584 015251 481719 137988 081693 478193 574750 440510 563475 631608 844128 > 4²⁰⁹ [i]