MinT - Best Known (121−55, 121, s)-Nets in Base 16

Best Known (121−55, 121, s)-Nets in Base 16

(121−55, 121, 524)-Net over F₁₆ — Constructive and digital

Digital (66, 121, 524)-net over F₁₆, using

1 times m-reduction [i] based on digital (66, 122, 524)-net over F₁₆, using
- trace code for nets [i] based on digital (5, 61, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(121−55, 121, 706)-Net over F₁₆ — Digital

Digital (66, 121, 706)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−55, 121, 163651)-Net in Base 16 — Upper bound on s

There is no (66, 121, 163652)-net in base 16, because

1 times m-reduction [i] would yield (66, 120, 163652)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 121886 731630 475684 457009 810185 574550 798561 743399 904492 784730 399477 072163 103435 390625 549567 143784 880024 268911 842139 412845 871343 348331 946088 759736 > 16¹²⁰ [i]