MinT - Best Known (98−76, 98, s)-Nets in Base 16

Best Known (98−76, 98, s)-Nets in Base 16

(98−76, 98, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 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]

(98−76, 98, 129)-Net over F₁₆ — Digital

Digital (22, 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]

(98−76, 98, 1255)-Net in Base 16 — Upper bound on s

There is no (22, 98, 1256)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10174 735135 622759 899566 773630 655816 855701 513037 450836 203034 565228 447300 632907 721349 612642 316685 216193 185051 601735 582221 > 16⁹⁸ [i]