MinT - Best Known (89−60, 89, s)-Nets in Base 16

Best Known (89−60, 89, s)-Nets in Base 16

(89−60, 89, 65)-Net over F₁₆ — Constructive and digital

Digital (29, 89, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 89, 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]

(89−60, 89, 120)-Net in Base 16 — Constructive

(29, 89, 120)-net in base 16, using

1 times m-reduction [i] based on (29, 90, 120)-net in base 16, using
- base change [i] based on digital (11, 72, 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]

(89−60, 89, 161)-Net over F₁₆ — Digital

Digital (29, 89, 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]

(89−60, 89, 2982)-Net in Base 16 — Upper bound on s

There is no (29, 89, 2983)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 148062 405523 869132 574570 018604 280152 459334 016566 435076 526829 213424 454016 861312 416923 012545 887109 539584 331476 > 16⁸⁹ [i]