MinT - Best Known (107−43, 107, s)-Nets in Base 16

Best Known (107−43, 107, s)-Nets in Base 16

(107−43, 107, 534)-Net over F₁₆ — Constructive and digital

Digital (64, 107, 534)-net over F₁₆, using

1 times m-reduction [i] based on digital (64, 108, 534)-net over F₁₆, using
- trace code for nets [i] based on digital (10, 54, 267)-net over F₂₅₆, using
  - net from sequence [i] based on digital (10, 266)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(107−43, 107, 1307)-Net over F₁₆ — Digital

Digital (64, 107, 1307)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−43, 107, 692361)-Net in Base 16 — Upper bound on s

There is no (64, 107, 692362)-net in base 16, because

1 times m-reduction [i] would yield (64, 106, 692362)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 323186 615180 988602 031358 125508 817015 155344 605309 405764 111191 358462 231505 547284 451748 165658 033310 287603 858732 113024 953590 812656 > 16¹⁰⁶ [i]