MinT - Best Known (206−95, 206, s)-Nets in Base 4

Best Known (206−95, 206, s)-Nets in Base 4

(206−95, 206, 130)-Net over F₄ — Constructive and digital

Digital (111, 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]

(206−95, 206, 190)-Net over F₄ — Digital

Digital (111, 206, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−95, 206, 2549)-Net in Base 4 — Upper bound on s

There is no (111, 206, 2550)-net in base 4, because

1 times m-reduction [i] would yield (111, 205, 2550)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2659 987834 927752 314646 820614 647804 629484 688451 607223 001626 075690 933623 181136 317037 460060 186588 483088 565660 327696 926594 907912 > 4²⁰⁵ [i]