MinT - Best Known (18, 18+36, s)-Nets in Base 16

Best Known (18, 18+36, s)-Nets in Base 16

(18, 18+36, 65)-Net over F₁₆ — Constructive and digital

Digital (18, 54, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 54, 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]

(18, 18+36, 98)-Net in Base 16 — Constructive

(18, 54, 98)-net in base 16, using

1 times m-reduction [i] based on (18, 55, 98)-net in base 16, using
- base change [i] based on digital (7, 44, 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]

(18, 18+36, 113)-Net over F₁₆ — Digital

Digital (18, 54, 113)-net over F₁₆, using

net from sequence [i] based on digital (18, 112)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 18 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(18, 18+36, 2052)-Net in Base 16 — Upper bound on s

There is no (18, 54, 2053)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 105464 480547 180548 786284 558489 247548 901809 527159 730702 004920 212736 > 16⁵⁴ [i]