MinT - Best Known (122−79, 122, s)-Nets in Base 16

Best Known (122−79, 122, s)-Nets in Base 16

(122−79, 122, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 122, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 122, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(122−79, 122, 226)-Net over F₁₆ — Digital

Digital (43, 122, 226)-net over F₁₆, using

net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
  - Drinfeld modules of rank 1 [i]

(122−79, 122, 5565)-Net in Base 16 — Upper bound on s

There is no (43, 122, 5566)-net in base 16, because

1 times m-reduction [i] would yield (43, 121, 5566)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 50 083905 965353 897908 885974 149956 276387 034219 669581 881570 724177 884027 483357 907667 564417 830753 171338 713246 045146 415605 685562 965662 803123 856547 769836 > 16¹²¹ [i]