MinT - Best Known (113−58, 113, s)-Nets in Base 16

Best Known (113−58, 113, s)-Nets in Base 16

(113−58, 113, 243)-Net over F₁₆ — Constructive and digital

Digital (55, 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]

(113−58, 113, 347)-Net over F₁₆ — Digital

Digital (55, 113, 347)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−58, 113, 38261)-Net in Base 16 — Upper bound on s

There is no (55, 113, 38262)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11630 894412 333587 269591 480214 521282 882173 725350 792122 100797 781087 332791 792691 407125 342182 608530 499032 137296 119489 163523 005662 043672 311396 > 16¹¹³ [i]