MinT - Best Known (48, 48+72, s)-Nets in Base 16

Best Known (48, 48+72, s)-Nets in Base 16

(48, 48+72, 243)-Net over F₁₆ — Constructive and digital

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]

(48, 48+72, 9806)-Net in Base 16 — Upper bound on s

There is no (48, 120, 9807)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 131334 880763 758054 912293 854489 863441 519900 303634 774181 296045 992737 944606 343351 308289 829339 297156 936432 275492 124136 692681 285815 298564 783778 445406 > 16¹²⁰ [i]