MinT - Best Known (113−51, 113, s)-Nets in Base 16

Best Known (113−51, 113, s)-Nets in Base 16

(113−51, 113, 524)-Net over F₁₆ — Constructive and digital

Digital (62, 113, 524)-net over F₁₆, using

1 times m-reduction [i] based on digital (62, 114, 524)-net over F₁₆, using
- trace code for nets [i] based on digital (5, 57, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(113−51, 113, 697)-Net over F₁₆ — Digital

Digital (62, 113, 697)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−51, 113, 168250)-Net in Base 16 — Upper bound on s

There is no (62, 113, 168251)-net in base 16, because

1 times m-reduction [i] would yield (62, 112, 168251)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 726 873803 323967 285794 517526 083194 661180 067079 768981 555496 225086 947642 941309 666554 363710 859045 410883 864485 681656 380258 908894 908142 236626 > 16¹¹² [i]