MinT - Best Known (117−93, 117, s)-Nets in Base 16

Best Known (117−93, 117, s)-Nets in Base 16

(117−93, 117, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 117, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 117, 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]

(117−93, 117, 129)-Net over F₁₆ — Digital

Digital (24, 117, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 117, 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]

(117−93, 117, 1279)-Net in Base 16 — Upper bound on s

There is no (24, 117, 1280)-net in base 16, because

1 times m-reduction [i] would yield (24, 116, 1280)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 48 361494 753618 949720 245485 154035 037842 137473 183459 479246 202605 037981 373415 458758 672670 316610 708664 187936 814855 593889 407980 054890 286424 548201 > 16¹¹⁶ [i]