MinT - Best Known (126−92, 126, s)-Nets in Base 16

Best Known (126−92, 126, s)-Nets in Base 16

(126−92, 126, 65)-Net over F₁₆ — Constructive and digital

Digital (34, 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]

(126−92, 126, 98)-Net in Base 16 — Constructive

(34, 126, 98)-net in base 16, using

t-expansion [i] based on (33, 126, 98)-net in base 16, using
- 4 times m-reduction [i] based on (33, 130, 98)-net in base 16, using
  - base change [i] based on digital (7, 104, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]

(126−92, 126, 193)-Net over F₁₆ — Digital

Digital (34, 126, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 126, 193)-net over F₁₆, using
- net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
    - a curve from the manYPoints database [i]

(126−92, 126, 2358)-Net in Base 16 — Upper bound on s

There is no (34, 126, 2359)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 52 468343 015197 526819 450859 182144 286113 382523 471779 896559 220527 520620 911498 887696 732740 318641 616582 635892 768202 019259 495017 845958 420398 437697 485836 807086 > 16¹²⁶ [i]