MinT - Best Known (51, 51+36, s)-Nets in Base 16

Best Known (51, 51+36, s)-Nets in Base 16

(51, 51+36, 528)-Net over F₁₆ — Constructive and digital

Digital (51, 87, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (51, 88, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 44, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(51, 51+36, 930)-Net over F₁₆ — Digital

Digital (51, 87, 930)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+36, 332613)-Net in Base 16 — Upper bound on s

There is no (51, 87, 332614)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 573 401816 771958 097453 013884 561063 729636 270645 227693 786720 045114 797687 203096 042376 339617 923943 432071 401656 > 16⁸⁷ [i]