MinT - Best Known (98−55, 98, s)-Nets in Base 16

Best Known (98−55, 98, s)-Nets in Base 16

(98−55, 98, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 98, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 98, 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]

(98−55, 98, 226)-Net over F₁₆ — Digital

Digital (43, 98, 226)-net over F₁₆, using

net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
  - Drinfeld modules of rank 1 [i]

(98−55, 98, 15410)-Net in Base 16 — Upper bound on s

There is no (43, 98, 15411)-net in base 16, because

1 times m-reduction [i] would yield (43, 97, 15411)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 631 198967 612428 659661 078622 499578 319672 218987 985184 542251 798014 246354 937258 613097 349455 662272 587678 082848 914812 345056 > 16⁹⁷ [i]