MinT - Best Known (56, 56+64, s)-Nets in Base 16

Best Known (56, 56+64, s)-Nets in Base 16

(56, 56+64, 243)-Net over F₁₆ — Constructive and digital

Digital (56, 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]

(56, 56+64, 303)-Net over F₁₆ — Digital

Digital (56, 120, 303)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+64, 27923)-Net in Base 16 — Upper bound on s

There is no (56, 120, 27924)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 124671 839765 925045 342511 456263 509525 596502 666681 968223 313169 424560 465380 201940 123941 401447 311112 064566 762976 178674 583126 026619 144707 820683 797896 > 16¹²⁰ [i]