MinT - Best Known (26, 26+72, s)-Nets in Base 16

Best Known (26, 26+72, s)-Nets in Base 16

(26, 26+72, 65)-Net over F₁₆ — Constructive and digital

Digital (26, 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]

(26, 26+72, 76)-Net in Base 16 — Constructive

(26, 98, 76)-net in base 16, using

7 times m-reduction [i] based on (26, 105, 76)-net in base 16, using
- base change [i] based on digital (5, 84, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(26, 26+72, 150)-Net over F₁₆ — Digital

Digital (26, 98, 150)-net over F₁₆, using

net from sequence [i] based on digital (26, 149)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 26 and N(F) ≥ 150, using
  - a curve from the manYPoints database [i]

(26, 26+72, 1785)-Net in Base 16 — Upper bound on s

There is no (26, 98, 1786)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10215 305222 604099 256290 062239 566680 392404 066110 484735 160632 666197 457590 098466 339199 656559 620840 969375 726379 280439 533066 > 16⁹⁸ [i]