MinT - Best Known (19, 53, s)-Nets in Base 49

Best Known (19, 53, s)-Nets in Base 49

(19, 53, 102)-Net over F₄₉ — Constructive and digital

Digital (19, 53, 102)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 18, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (1, 35, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(19, 53, 138)-Net over F₄₉ — Digital

Digital (19, 53, 138)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(19, 53, 27797)-Net in Base 49 — Upper bound on s

There is no (19, 53, 27798)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 380610 906081 230081 393938 433696 875462 864947 017761 152858 311884 548904 348588 723973 384202 995233 > 49⁵³ [i]