MinT - Best Known (206−90, 206, s)-Nets in Base 4

Best Known (206−90, 206, s)-Nets in Base 4

(206−90, 206, 130)-Net over F₄ — Constructive and digital

Digital (116, 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]

(206−90, 206, 226)-Net over F₄ — Digital

Digital (116, 206, 226)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−90, 206, 3313)-Net in Base 4 — Upper bound on s

There is no (116, 206, 3314)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10582 460243 980716 018772 725576 355525 164343 211629 002339 439925 039171 761488 614869 693592 478777 609639 382488 972499 169400 092326 870660 > 4²⁰⁶ [i]