MinT - Best Known (98−84, 98, s)-Nets in Base 16

Best Known (98−84, 98, s)-Nets in Base 16

(98−84, 98, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 98, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 98, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(98−84, 98, 97)-Net over F₁₆ — Digital

Digital (14, 98, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 98, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(98−84, 98, 686)-Net in Base 16 — Upper bound on s

There is no (14, 98, 687)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10089 866309 108351 311287 758048 091551 108303 093660 389867 232498 444194 473537 716323 305501 949055 187829 090067 290671 721083 760861 > 16⁹⁸ [i]