MinT - Best Known (123−79, 123, s)-Nets in Base 16

Best Known (123−79, 123, s)-Nets in Base 16

(123−79, 123, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 123, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 123, 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]

(123−79, 123, 226)-Net over F₁₆ — Digital

Digital (44, 123, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 123, 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]

(123−79, 123, 5977)-Net in Base 16 — Upper bound on s

There is no (44, 123, 5978)-net in base 16, because

1 times m-reduction [i] would yield (44, 122, 5978)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 802 951010 825020 561629 865472 438788 262340 595907 281174 155651 034083 282548 874738 228162 893094 783448 089250 788583 029374 459222 715887 708473 161897 950015 826856 > 16¹²² [i]