MinT - Best Known (25, 25+96, s)-Nets in Base 16

Best Known (25, 25+96, s)-Nets in Base 16

(25, 25+96, 65)-Net over F₁₆ — Constructive and digital

Digital (25, 121, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 121, 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]

(25, 25+96, 66)-Net in Base 16 — Constructive

(25, 121, 66)-net in base 16, using

net from sequence [i] based on (25, 65)-sequence in base 16, using
- base expansion [i] based on digital (50, 65)-sequence over F₄, using
  - t-expansion [i] based on digital (49, 65)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
      - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(25, 25+96, 144)-Net over F₁₆ — Digital

Digital (25, 121, 144)-net over F₁₆, using

net from sequence [i] based on digital (25, 143)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 25 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(25, 25+96, 1328)-Net in Base 16 — Upper bound on s

There is no (25, 121, 1329)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 50 157658 802841 917016 453091 419455 480493 131896 638351 590819 519410 752773 814235 256606 847799 744004 854570 072570 452275 398216 132935 258826 544956 827669 119881 > 16¹²¹ [i]