MinT - Best Known (23, 23+85, s)-Nets in Base 16

Best Known (23, 23+85, s)-Nets in Base 16

(23, 23+85, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 108, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 108, 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+85, 129)-Net over F₁₆ — Digital

Digital (23, 108, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 108, 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+85, 1263)-Net in Base 16 — Upper bound on s

There is no (23, 108, 1264)-net in base 16, because

1 times m-reduction [i] would yield (23, 107, 1264)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 713 230795 490953 800086 529962 945103 837663 747004 039601 904572 855249 940166 439223 034817 137679 501944 337845 034307 723813 900352 654662 109321 > 16¹⁰⁷ [i]