MinT - Best Known (113−60, 113, s)-Nets in Base 16

Best Known (113−60, 113, s)-Nets in Base 16

(113−60, 113, 243)-Net over F₁₆ — Constructive and digital

Digital (53, 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]

(113−60, 113, 294)-Net over F₁₆ — Digital

Digital (53, 113, 294)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−60, 113, 27539)-Net in Base 16 — Upper bound on s

There is no (53, 113, 27540)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11635 852577 987736 098297 622429 114053 921794 827264 733004 692631 142457 078642 370169 300296 757865 298070 030013 117008 056053 475341 787515 241801 097376 > 16¹¹³ [i]