MinT - Best Known (47−30, 47, s)-Nets in Base 49

Best Known (47−30, 47, s)-Nets in Base 49

(47−30, 47, 102)-Net over F₄₉ — Constructive and digital

Digital (17, 47, 102)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 16, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (1, 31, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(47−30, 47, 131)-Net over F₄₉ — Digital

Digital (17, 47, 131)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(47−30, 47, 26445)-Net in Base 49 — Upper bound on s

There is no (17, 47, 26446)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 27 499182 155182 844262 884420 142416 388543 965937 191814 672423 813633 738354 303476 450401 > 49⁴⁷ [i]