MinT - Best Known (115−92, 115, s)-Nets in Base 16

Best Known (115−92, 115, s)-Nets in Base 16

(115−92, 115, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 115, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 115, 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]

(115−92, 115, 129)-Net over F₁₆ — Digital

Digital (23, 115, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 115, 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]

(115−92, 115, 1203)-Net in Base 16 — Upper bound on s

There is no (23, 115, 1204)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 062664 822183 578662 260593 555005 369286 014734 632911 724116 068134 786026 919630 872688 520049 820689 993704 499000 348292 858787 472360 243712 041526 887636 > 16¹¹⁵ [i]