MinT - Best Known (112−46, 112, s)-Nets in Base 16

Best Known (112−46, 112, s)-Nets in Base 16

(112−46, 112, 534)-Net over F₁₆ — Constructive and digital

Digital (66, 112, 534)-net over F₁₆, using

trace code for nets [i] based on digital (10, 56, 267)-net over F₂₅₆, using
- net from sequence [i] based on digital (10, 266)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(112−46, 112, 1189)-Net over F₁₆ — Digital

Digital (66, 112, 1189)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−46, 112, 459085)-Net in Base 16 — Upper bound on s

There is no (66, 112, 459086)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 726 842562 461228 650662 920067 359118 419172 108615 199878 089864 480796 852575 233311 735338 337249 483739 322379 214199 181432 620258 194389 358726 030096 > 16¹¹² [i]