MinT - Best Known (106−70, 106, s)-Nets in Base 16

Best Known (106−70, 106, s)-Nets in Base 16

(106−70, 106, 65)-Net over F₁₆ — Constructive and digital

Digital (36, 106, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 106, 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]

(106−70, 106, 120)-Net in Base 16 — Constructive

(36, 106, 120)-net in base 16, using

19 times m-reduction [i] based on (36, 125, 120)-net in base 16, using
- base change [i] based on digital (11, 100, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]

(106−70, 106, 193)-Net over F₁₆ — Digital

Digital (36, 106, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 106, 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]

(106−70, 106, 4091)-Net in Base 16 — Upper bound on s

There is no (36, 106, 4092)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 478219 374656 780964 853201 833317 000843 896456 815663 726444 611538 105603 413389 957663 877133 271534 994459 915849 488022 856308 863669 623051 > 16¹⁰⁶ [i]