MinT - Best Known (130−97, 130, s)-Nets in Base 16

Best Known (130−97, 130, s)-Nets in Base 16

(130−97, 130, 65)-Net over F₁₆ — Constructive and digital

Digital (33, 130, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 130, 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]

(130−97, 130, 98)-Net in Base 16 — Constructive

(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]

(130−97, 130, 193)-Net over F₁₆ — Digital

Digital (33, 130, 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]

(130−97, 130, 2125)-Net in Base 16 — Upper bound on s

There is no (33, 130, 2126)-net in base 16, because

1 times m-reduction [i] would yield (33, 129, 2126)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 219225 218042 763464 275867 612665 788635 541169 303348 669591 153111 794190 545302 801876 576013 077552 121783 037417 987704 959614 823979 815160 490729 427924 332157 145777 905396 > 16¹²⁹ [i]