MinT - Best Known (39−22, 39, s)-Nets in Base 49

Best Known (39−22, 39, s)-Nets in Base 49

(39−22, 39, 106)-Net over F₄₉ — Constructive and digital

Digital (17, 39, 106)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 14, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (3, 25, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉ (see above)

(39−22, 39, 260)-Net over F₄₉ — Digital

Digital (17, 39, 260)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(39−22, 39, 100522)-Net in Base 49 — Upper bound on s

There is no (17, 39, 100523)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 827306 138216 682220 364791 179487 162812 007114 179975 799727 467090 636465 > 49³⁹ [i]