MinT - Best Known (16, 109, s)-Nets in Base 16

Best Known (16, 109, s)-Nets in Base 16

(16, 109, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 109, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 109, 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]

(16, 109, 98)-Net over F₁₆ — Digital

Digital (16, 109, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 109, 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]

(16, 109, 780)-Net in Base 16 — Upper bound on s

There is no (16, 109, 781)-net in base 16, because

1 times m-reduction [i] would yield (16, 108, 781)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11485 707802 322176 555134 755232 816464 905402 090141 461266 808797 155959 222253 272570 821745 014227 516268 021925 832068 933904 596590 363925 318016 > 16¹⁰⁸ [i]