MinT - Best Known (118−71, 118, s)-Nets in Base 16

Best Known (118−71, 118, s)-Nets in Base 16

(118−71, 118, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 118, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 118, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(118−71, 118, 243)-Net over F₁₆ — Digital

Digital (47, 118, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 118, 243)-net over F₁₆, using
- net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
    - a curve from the manYPoints database [i]

(118−71, 118, 9806)-Net in Base 16 — Upper bound on s

There is no (47, 118, 9807)-net in base 16, because

1 times m-reduction [i] would yield (47, 117, 9807)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 763 218644 415089 238214 879079 730613 306255 138050 544941 700534 798450 082877 120963 141423 431492 607952 332273 795646 924629 955295 416827 049793 098191 317176 > 16¹¹⁷ [i]