MinT - Best Known (109−47, 109, s)-Nets in Base 16

Best Known (109−47, 109, s)-Nets in Base 16

(109−47, 109, 528)-Net over F₁₆ — Constructive and digital

Digital (62, 109, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (62, 110, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 55, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(109−47, 109, 879)-Net over F₁₆ — Digital

Digital (62, 109, 879)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−47, 109, 283448)-Net in Base 16 — Upper bound on s

There is no (62, 109, 283449)-net in base 16, because

1 times m-reduction [i] would yield (62, 108, 283449)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11090 970791 849447 055887 298003 248968 972869 653021 539891 296379 963980 392648 619657 734133 341738 227780 597534 381337 028099 120520 620602 153656 > 16¹⁰⁸ [i]