MinT - Best Known (116−105, 116, s)-Nets in Base 16

Best Known (116−105, 116, s)-Nets in Base 16

(116−105, 116, 65)-Net over F₁₆ — Constructive and digital

Digital (11, 116, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 116, 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]

(116−105, 116, 81)-Net over F₁₆ — Digital

Digital (11, 116, 81)-net over F₁₆, using

t-expansion [i] based on digital (10, 116, 81)-net over F₁₆, using
- net from sequence [i] based on digital (10, 80)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 10 and N(F) ≥ 81, using
    - a curve from the manYPoints database [i]

(116−105, 116, 547)-Net in Base 16 — Upper bound on s

There is no (11, 116, 548)-net in base 16, because

37 times m-reduction [i] would yield (11, 79, 548)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 134485 286719 841638 432777 712364 408345 334213 451899 253160 450836 745455 844856 533056 249636 975953 401331 > 16⁷⁹ [i]