MinT - Best Known (118−95, 118, s)-Nets in Base 16

Best Known (118−95, 118, s)-Nets in Base 16

(118−95, 118, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 118, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 118, 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]

(118−95, 118, 129)-Net over F₁₆ — Digital

Digital (23, 118, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 118, 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]

(118−95, 118, 1191)-Net in Base 16 — Upper bound on s

There is no (23, 118, 1192)-net in base 16, because

1 times m-reduction [i] would yield (23, 117, 1192)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 774 407618 668082 524837 455837 881516 076973 737728 849214 531388 854987 653185 968585 878050 552334 607497 820985 951181 965600 446948 329823 031460 382686 687536 > 16¹¹⁷ [i]