MinT - Best Known (206−85, 206, s)-Nets in Base 4

Best Known (206−85, 206, s)-Nets in Base 4

(206−85, 206, 130)-Net over F₄ — Constructive and digital

Digital (121, 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]

(206−85, 206, 271)-Net over F₄ — Digital

Digital (121, 206, 271)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−85, 206, 4744)-Net in Base 4 — Upper bound on s

There is no (121, 206, 4745)-net in base 4, because

1 times m-reduction [i] would yield (121, 205, 4745)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2661 431189 742330 177732 757534 097299 635253 534856 537126 905381 741035 968861 606430 444066 279838 258004 114961 927691 417153 057457 575552 > 4²⁰⁵ [i]