MinT - Best Known (205−99, 205, s)-Nets in Base 4

Best Known (205−99, 205, s)-Nets in Base 4

(205−99, 205, 130)-Net over F₄ — Constructive and digital

Digital (106, 205, 130)-net over F₄, using

t-expansion [i] based on digital (105, 205, 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]

(205−99, 205, 164)-Net over F₄ — Digital

Digital (106, 205, 164)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−99, 205, 2005)-Net in Base 4 — Upper bound on s

There is no (106, 205, 2006)-net in base 4, because

1 times m-reduction [i] would yield (106, 204, 2006)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 675 378769 746886 626413 720139 234629 236089 668369 999598 743814 671389 808248 008554 860831 531196 895080 699417 180872 355241 277965 500146 > 4²⁰⁴ [i]