MinT - Best Known (118−97, 118, s)-Nets in Base 16

Best Known (118−97, 118, s)-Nets in Base 16

(118−97, 118, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 118, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 118, 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]

(118−97, 118, 129)-Net over F₁₆ — Digital

Digital (21, 118, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 118, 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]

(118−97, 118, 1049)-Net in Base 16 — Upper bound on s

There is no (21, 118, 1050)-net in base 16, because

1 times m-reduction [i] would yield (21, 117, 1050)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 786 813926 404912 307357 570914 362977 371824 153076 822539 086899 792307 318939 276794 612482 953739 048393 050508 787230 543410 674124 874399 086842 572068 385376 > 16¹¹⁷ [i]