MinT - Best Known (123−100, 123, s)-Nets in Base 16

Best Known (123−100, 123, s)-Nets in Base 16

(123−100, 123, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 123, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 123, 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]

(123−100, 123, 129)-Net over F₁₆ — Digital

Digital (23, 123, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 123, 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]

(123−100, 123, 1162)-Net in Base 16 — Upper bound on s

There is no (23, 123, 1163)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12916 004563 074110 589064 323295 202963 883024 965956 356504 122797 997524 506064 707612 620026 837046 192935 647341 982801 095206 929934 379165 204444 829325 223707 860376 > 16¹²³ [i]