MinT - Best Known (113−64, 113, s)-Nets in Base 16

Best Known (113−64, 113, s)-Nets in Base 16

(113−64, 113, 243)-Net over F₁₆ — Constructive and digital

Digital (49, 113, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 113, 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]

(113−64, 113, 15217)-Net in Base 16 — Upper bound on s

There is no (49, 113, 15218)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11648 775393 345004 270218 645020 013708 450191 852068 933308 318202 254784 094977 712960 003099 558204 756647 034228 710599 606085 166382 448791 108831 258241 > 16¹¹³ [i]