MinT - Best Known (13, 13+20, s)-Nets in Base 49

Best Known (13, 13+20, s)-Nets in Base 49

(13, 13+20, 103)-Net over F₄₉ — Constructive and digital

Digital (13, 33, 103)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 11, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (2, 22, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(13, 13+20, 152)-Net over F₄₉ — Digital

Digital (13, 33, 152)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(13, 13+20, 35671)-Net in Base 49 — Upper bound on s

There is no (13, 33, 35672)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 59 771905 714769 656734 992458 869210 321473 916997 640142 455041 > 49³³ [i]