MinT - Best Known (206−93, 206, s)-Nets in Base 4

Best Known (206−93, 206, s)-Nets in Base 4

(206−93, 206, 130)-Net over F₄ — Constructive and digital

Digital (113, 206, 130)-net over F₄, using

t-expansion [i] based on digital (105, 206, 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]

(206−93, 206, 203)-Net over F₄ — Digital

Digital (113, 206, 203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−93, 206, 2854)-Net in Base 4 — Upper bound on s

There is no (113, 206, 2855)-net in base 4, because

1 times m-reduction [i] would yield (113, 205, 2855)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2670 456824 501156 295117 472296 428769 193878 203044 268749 817264 008986 570233 804789 174357 284411 539532 007297 880937 753301 353124 489056 > 4²⁰⁵ [i]