MinT - Best Known (88−74, 88, s)-Nets in Base 16

Best Known (88−74, 88, s)-Nets in Base 16

(88−74, 88, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 88, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 88, 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]

(88−74, 88, 97)-Net over F₁₆ — Digital

Digital (14, 88, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 88, 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]

(88−74, 88, 693)-Net in Base 16 — Upper bound on s

There is no (14, 88, 694)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9347 886488 654325 614726 384229 987107 504468 339396 197814 892614 092647 276628 179101 392053 502320 970342 765979 122921 > 16⁸⁸ [i]