MinT - Best Known (20, 20+89, s)-Nets in Base 16

Best Known (20, 20+89, s)-Nets in Base 16

(20, 20+89, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 109, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 109, 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]

(20, 20+89, 129)-Net over F₁₆ — Digital

Digital (20, 109, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 109, 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]

(20, 20+89, 1014)-Net in Base 16 — Upper bound on s

There is no (20, 109, 1015)-net in base 16, because

1 times m-reduction [i] would yield (20, 108, 1015)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11478 091948 265698 693642 228628 537581 878733 941948 419522 541611 905250 088901 376568 033039 103517 582322 130264 131602 629073 574702 931669 332526 > 16¹⁰⁸ [i]