MinT - Best Known (130−96, 130, s)-Nets in Base 16

Best Known (130−96, 130, s)-Nets in Base 16

(130−96, 130, 65)-Net over F₁₆ — Constructive and digital

Digital (34, 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]

(130−96, 130, 98)-Net in Base 16 — Constructive

(34, 130, 98)-net in base 16, using

t-expansion [i] based on (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]

(130−96, 130, 193)-Net over F₁₆ — Digital

Digital (34, 130, 193)-net over F₁₆, using

t-expansion [i] based on 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]

(130−96, 130, 2252)-Net in Base 16 — Upper bound on s

There is no (34, 130, 2253)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 434764 364221 984421 113370 774069 373145 109132 992019 998962 772368 850297 165130 794894 647487 694642 540970 404230 254240 263713 275450 255443 738767 107763 001599 092833 081836 > 16¹³⁰ [i]