MinT - Best Known (98−74, 98, s)-Nets in Base 16

Best Known (98−74, 98, s)-Nets in Base 16

(98−74, 98, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 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]

(98−74, 98, 129)-Net over F₁₆ — Digital

Digital (24, 98, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 98, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(98−74, 98, 1490)-Net in Base 16 — Upper bound on s

There is no (24, 98, 1491)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10319 430459 227892 150870 427176 366443 465434 281122 161179 369456 657053 832188 475452 719613 116552 143620 735632 006529 928418 395856 > 16⁹⁸ [i]