MinT - Best Known (126−103, 126, s)-Nets in Base 16

Best Known (126−103, 126, s)-Nets in Base 16

(126−103, 126, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 126, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 126, 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]

(126−103, 126, 129)-Net over F₁₆ — Digital

Digital (23, 126, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 126, 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]

(126−103, 126, 1154)-Net in Base 16 — Upper bound on s

There is no (23, 126, 1155)-net in base 16, because

1 times m-reduction [i] would yield (23, 125, 1155)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 285435 410158 112178 702407 287244 986235 114740 733095 915658 448375 281420 462918 878375 827025 076816 446887 085700 226446 355221 230315 481456 686750 048698 122747 608576 > 16¹²⁵ [i]