MinT - Best Known (95−49, 95, s)-Nets in Base 16

Best Known (95−49, 95, s)-Nets in Base 16

(95−49, 95, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 95, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 95, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(95−49, 95, 294)-Net over F₁₆ — Digital

Digital (46, 95, 294)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−49, 95, 33981)-Net in Base 16 — Upper bound on s

There is no (46, 95, 33982)-net in base 16, because

1 times m-reduction [i] would yield (46, 94, 33982)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 153984 109885 537111 555119 827627 644055 260624 855505 278826 793265 478393 446958 987299 826424 222213 766559 113232 079548 251321 > 16⁹⁴ [i]