MinT - Best Known (36−21, 36, s)-Nets in Base 49

Best Known (36−21, 36, s)-Nets in Base 49

(36−21, 36, 105)-Net over F₄₉ — Constructive and digital

Digital (15, 36, 105)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 12, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (3, 24, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(36−21, 36, 201)-Net over F₄₉ — Digital

Digital (15, 36, 201)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(36−21, 36, 77695)-Net in Base 49 — Upper bound on s

There is no (15, 36, 77696)-net in base 49, because

1 times m-reduction [i] would yield (15, 35, 77696)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 143515 601803 389487 757621 022467 134475 745259 087263 098299 207681 > 49³⁵ [i]