MinT - Best Known (42, 42+29, s)-Nets in Base 16

Best Known (42, 42+29, s)-Nets in Base 16

(42, 42+29, 526)-Net over F₁₆ — Constructive and digital

Digital (42, 71, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (42, 72, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 36, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(42, 42+29, 866)-Net over F₁₆ — Digital

Digital (42, 71, 866)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+29, 422628)-Net in Base 16 — Upper bound on s

There is no (42, 71, 422629)-net in base 16, because

1 times m-reduction [i] would yield (42, 70, 422629)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 942702 643951 949919 895686 226385 394592 437867 444522 138147 936367 757713 151376 903017 811216 > 16⁷⁰ [i]