MinT - Best Known (23, 23+83, s)-Nets in Base 16

Best Known (23, 23+83, s)-Nets in Base 16

(23, 23+83, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 106, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 106, 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+83, 129)-Net over F₁₆ — Digital

Digital (23, 106, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 106, 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+83, 1282)-Net in Base 16 — Upper bound on s

There is no (23, 106, 1283)-net in base 16, because

1 times m-reduction [i] would yield (23, 105, 1283)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 779798 989818 673126 781755 405939 940352 946355 742103 175367 916022 953330 263056 424394 223415 327819 675683 292469 507010 148440 117013 087296 > 16¹⁰⁵ [i]