MinT - Best Known (130−98, 130, s)-Nets in Base 16

Best Known (130−98, 130, s)-Nets in Base 16

(130−98, 130, 65)-Net over F₁₆ — Constructive and digital

Digital (32, 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]

(130−98, 130, 76)-Net in Base 16 — Constructive

(32, 130, 76)-net in base 16, using

t-expansion [i] based on (31, 130, 76)-net in base 16, using
- base change [i] based on digital (5, 104, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(130−98, 130, 168)-Net over F₁₆ — Digital

Digital (32, 130, 168)-net over F₁₆, using

t-expansion [i] based on digital (31, 130, 168)-net over F₁₆, using
- net from sequence [i] based on digital (31, 167)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 31 and N(F) ≥ 168, using
    - a curve from the manYPoints database [i]

(130−98, 130, 1967)-Net in Base 16 — Upper bound on s

There is no (32, 130, 1968)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 494906 387588 751352 063086 591120 646178 557004 924044 009329 336963 656483 027228 086356 657420 993001 728565 076358 099739 728931 116155 812728 042710 746452 855196 826832 112456 > 16¹³⁰ [i]