MinT - Best Known (130−106, 130, s)-Nets in Base 16

Best Known (130−106, 130, s)-Nets in Base 16

(130−106, 130, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 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]

(130−106, 130, 129)-Net over F₁₆ — Digital

Digital (24, 130, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 130, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(130−106, 130, 1204)-Net in Base 16 — Upper bound on s

There is no (24, 130, 1205)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 534573 043165 624780 084614 491313 544313 994606 077149 133489 048879 265552 134414 275081 975542 547698 774435 949107 039895 156011 440501 009360 843881 984407 334429 854846 984976 > 16¹³⁰ [i]