MinT - Best Known (122−103, 122, s)-Nets in Base 16

Best Known (122−103, 122, s)-Nets in Base 16

(122−103, 122, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 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]

(122−103, 122, 129)-Net over F₁₆ — Digital

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]

(122−103, 122, 923)-Net in Base 16 — Upper bound on s

There is no (19, 122, 924)-net in base 16, because

1 times m-reduction [i] would yield (19, 121, 924)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 50 696619 196343 193771 351487 536243 943274 949186 801343 679579 468226 758960 490886 612720 846246 846721 113936 177277 773187 406740 096556 044804 549930 489970 566236 > 16¹²¹ [i]