MinT - Best Known (103−87, 103, s)-Nets in Base 16

Best Known (103−87, 103, s)-Nets in Base 16

(103−87, 103, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 103, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 103, 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]

(103−87, 103, 98)-Net over F₁₆ — Digital

Digital (16, 103, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 103, 98)-net over F₁₆, using
- net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
    - a curve from the manYPoints database [i]

(103−87, 103, 784)-Net in Base 16 — Upper bound on s

There is no (16, 103, 785)-net in base 16, because

1 times m-reduction [i] would yield (16, 102, 785)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 669 095497 666695 712026 966945 423827 016205 760635 761940 432240 867901 417488 016307 739415 675007 284632 626140 432608 118836 020878 536576 > 16¹⁰² [i]