MinT - Best Known (39−24, 39, s)-Nets in Base 49

Best Known (39−24, 39, s)-Nets in Base 49

(39−24, 39, 103)-Net over F₄₉ — Constructive and digital

Digital (15, 39, 103)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 13, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (2, 26, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(39−24, 39, 149)-Net over F₄₉ — Digital

Digital (15, 39, 149)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(39−24, 39, 34291)-Net in Base 49 — Upper bound on s

There is no (15, 39, 34292)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 827456 966381 252537 739616 699966 951728 916025 665730 216406 205831 743745 > 49³⁹ [i]