MinT - Best Known (79−60, 79, s)-Nets in Base 16

Best Known (79−60, 79, s)-Nets in Base 16

(79−60, 79, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 79, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 79, 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]

(79−60, 79, 129)-Net over F₁₆ — Digital

Digital (19, 79, 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]

(79−60, 79, 1173)-Net in Base 16 — Upper bound on s

There is no (19, 79, 1174)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 134999 895044 657108 501385 292676 841713 504091 002065 325256 855833 679945 717131 030040 851721 539679 050176 > 16⁷⁹ [i]