MinT - Best Known (54, 54+66, s)-Nets in Base 16

Best Known (54, 54+66, s)-Nets in Base 16

(54, 54+66, 243)-Net over F₁₆ — Constructive and digital

Digital (54, 120, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 120, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(54, 54+66, 260)-Net over F₁₆ — Digital

Digital (54, 120, 260)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+66, 273)-Net in Base 16

(54, 120, 273)-net in base 16, using

base change [i] based on digital (30, 96, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(54, 54+66, 20965)-Net in Base 16 — Upper bound on s

There is no (54, 120, 20966)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 124445 266978 078813 248688 836346 950356 325377 473383 277606 500418 874625 102568 167295 324181 787293 842928 562695 567404 333101 889362 755428 904665 065222 117721 > 16¹²⁰ [i]