MinT - Best Known (123−103, 123, s)-Nets in Base 16

Best Known (123−103, 123, s)-Nets in Base 16

(123−103, 123, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 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]

(123−103, 123, 129)-Net over F₁₆ — Digital

Digital (20, 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]

(123−103, 123, 976)-Net in Base 16 — Upper bound on s

There is no (20, 123, 977)-net in base 16, because

1 times m-reduction [i] would yield (20, 122, 977)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 803 463359 361857 442300 701458 465352 472076 027759 019230 378521 087469 922474 510302 400535 936227 512386 879987 623390 442167 291693 289727 831979 185557 957071 198656 > 16¹²² [i]