MinT - Best Known (110−87, 110, s)-Nets in Base 16

Best Known (110−87, 110, s)-Nets in Base 16

(110−87, 110, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 110, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 110, 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]

(110−87, 110, 129)-Net over F₁₆ — Digital

Digital (23, 110, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 110, 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]

(110−87, 110, 1245)-Net in Base 16 — Upper bound on s

There is no (23, 110, 1246)-net in base 16, because

1 times m-reduction [i] would yield (23, 109, 1246)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 178135 356315 666797 863628 348921 518960 038176 050931 618105 452230 154654 094617 450307 564747 788041 703813 560452 912773 916502 528884 750329 628596 > 16¹⁰⁹ [i]