MinT - Best Known (122−100, 122, s)-Nets in Base 16

Best Known (122−100, 122, s)-Nets in Base 16

(122−100, 122, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 122, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 122, 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]

(122−100, 122, 129)-Net over F₁₆ — Digital

Digital (22, 122, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 122, 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]

(122−100, 122, 1098)-Net in Base 16 — Upper bound on s

There is no (22, 122, 1099)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 815 125842 161851 166110 957148 693661 179352 447889 669335 770340 744320 201497 085183 024958 262141 638514 937298 168896 031424 794730 810983 396414 876739 446995 089876 > 16¹²² [i]