MinT - Best Known (21, 21+103, s)-Nets in Base 16

Best Known (21, 21+103, s)-Nets in Base 16

(21, 21+103, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 124, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 124, 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]

(21, 21+103, 129)-Net over F₁₆ — Digital

Digital (21, 124, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 124, 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]

(21, 21+103, 1033)-Net in Base 16 — Upper bound on s

There is no (21, 124, 1034)-net in base 16, because

1 times m-reduction [i] would yield (21, 123, 1034)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13391 354371 450046 105460 198069 036180 812529 259873 777918 123044 342921 546418 985640 066593 451410 321778 926710 544900 794270 378225 334197 586742 063600 043327 419136 > 16¹²³ [i]