MinT - Best Known (99−70, 99, s)-Nets in Base 16

Best Known (99−70, 99, s)-Nets in Base 16

(99−70, 99, 65)-Net over F₁₆ — Constructive and digital

Digital (29, 99, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 99, 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]

(99−70, 99, 104)-Net in Base 16 — Constructive

(29, 99, 104)-net in base 16, using

1 times m-reduction [i] based on (29, 100, 104)-net in base 16, using
- base change [i] based on digital (9, 80, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(99−70, 99, 161)-Net over F₁₆ — Digital

Digital (29, 99, 161)-net over F₁₆, using

net from sequence [i] based on digital (29, 160)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 29 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(99−70, 99, 2341)-Net in Base 16 — Upper bound on s

There is no (29, 99, 2342)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 161887 406941 007151 864855 320088 776011 178399 115676 442097 097167 928019 629088 373373 776386 458688 574753 491236 365344 309934 719926 > 16⁹⁹ [i]