MinT - Best Known (122−101, 122, s)-Nets in Base 16

Best Known (122−101, 122, s)-Nets in Base 16

(122−101, 122, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 122, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 122, 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]

(122−101, 122, 129)-Net over F₁₆ — Digital

Digital (21, 122, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 122, 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]

(122−101, 122, 1037)-Net in Base 16 — Upper bound on s

There is no (21, 122, 1038)-net in base 16, because

1 times m-reduction [i] would yield (21, 121, 1038)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 50 387672 088798 087058 037252 540542 145604 030838 003763 375795 235369 558218 672540 268200 009543 596852 549295 132933 063710 187042 247548 700618 332367 851674 485376 > 16¹²¹ [i]