MinT - Best Known (36, 36+68, s)-Nets in Base 16

Best Known (36, 36+68, s)-Nets in Base 16

(36, 36+68, 65)-Net over F₁₆ — Constructive and digital

Digital (36, 104, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 104, 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]

(36, 36+68, 120)-Net in Base 16 — Constructive

(36, 104, 120)-net in base 16, using

21 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]

(36, 36+68, 193)-Net over F₁₆ — Digital

Digital (36, 104, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 104, 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]

(36, 36+68, 4332)-Net in Base 16 — Upper bound on s

There is no (36, 104, 4333)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 170411 972930 148932 010244 124272 845731 946510 456951 411702 204269 899944 876279 137541 593186 248799 903708 844232 554575 535954 105661 565806 > 16¹⁰⁴ [i]