MinT - Best Known (62, 62+43, s)-Nets in Base 16

Best Known (62, 62+43, s)-Nets in Base 16

(62, 62+43, 532)-Net over F₁₆ — Constructive and digital

Digital (62, 105, 532)-net over F₁₆, using

1 times m-reduction [i] based on digital (62, 106, 532)-net over F₁₆, using
- trace code for nets [i] based on digital (9, 53, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(62, 62+43, 1148)-Net over F₁₆ — Digital

Digital (62, 105, 1148)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+43, 531683)-Net in Base 16 — Upper bound on s

There is no (62, 105, 531684)-net in base 16, because

1 times m-reduction [i] would yield (62, 104, 531684)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 169236 287801 032314 772128 462939 840115 992815 179455 197573 186044 727914 728595 810546 818290 449803 395545 132688 592665 184578 460734 347336 > 16¹⁰⁴ [i]