MinT - Best Known (61, 61+46, s)-Nets in Base 16

Best Known (61, 61+46, s)-Nets in Base 16

(61, 61+46, 528)-Net over F₁₆ — Constructive and digital

Digital (61, 107, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (61, 108, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 54, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(61, 61+46, 880)-Net over F₁₆ — Digital

Digital (61, 107, 880)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+46, 251257)-Net in Base 16 — Upper bound on s

There is no (61, 107, 251258)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 693 203009 619909 883011 395396 570162 930159 805762 916724 860400 352176 539129 770788 157519 638019 296606 699187 687750 920592 353595 456177 891436 > 16¹⁰⁷ [i]