MinT - Best Known (122−99, 122, s)-Nets in Base 16

Best Known (122−99, 122, s)-Nets in Base 16

(122−99, 122, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 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]

(122−99, 122, 129)-Net over F₁₆ — Digital

Digital (23, 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]

(122−99, 122, 1171)-Net in Base 16 — Upper bound on s

There is no (23, 122, 1172)-net in base 16, because

1 times m-reduction [i] would yield (23, 121, 1172)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 51 113977 444573 949120 887280 213496 002414 794969 662149 149583 828266 020663 716575 372892 718555 235514 394875 194645 832018 047578 352409 343059 299435 056507 308596 > 16¹²¹ [i]