MinT - Best Known (21, 21+107, s)-Nets in Base 16

Best Known (21, 21+107, s)-Nets in Base 16

(21, 21+107, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 128, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 128, 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+107, 129)-Net over F₁₆ — Digital

Digital (21, 128, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 128, 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+107, 1025)-Net in Base 16 — Upper bound on s

There is no (21, 128, 1026)-net in base 16, because

1 times m-reduction [i] would yield (21, 127, 1026)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 874 015603 562751 232294 823564 469693 542436 073701 843442 140874 530981 167028 439154 996591 938699 983691 918847 196780 478363 347888 388076 475473 101122 251257 909906 084096 > 16¹²⁷ [i]