MinT - Best Known (16, 44, s)-Nets in Base 49

Best Known (16, 44, s)-Nets in Base 49

(16, 44, 102)-Net over F₄₉ — Constructive and digital

Digital (16, 44, 102)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 15, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (1, 29, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(16, 44, 128)-Net over F₄₉ — Digital

Digital (16, 44, 128)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(16, 44, 25831)-Net in Base 49 — Upper bound on s

There is no (16, 44, 25832)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 233 765105 591145 369879 379590 797713 852886 066290 017564 145228 439885 338001 497345 > 49⁴⁴ [i]