MinT - Best Known (23, 23+81, s)-Nets in Base 16

Best Known (23, 23+81, s)-Nets in Base 16

(23, 23+81, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 104, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 104, 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]

(23, 23+81, 129)-Net over F₁₆ — Digital

Digital (23, 104, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 104, 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]

(23, 23+81, 1303)-Net in Base 16 — Upper bound on s

There is no (23, 104, 1304)-net in base 16, because

1 times m-reduction [i] would yield (23, 103, 1304)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10832 516475 420168 974461 118180 532387 163421 084892 452349 715079 671407 042032 006521 513687 053185 308910 141646 093261 802124 085485 921776 > 16¹⁰³ [i]