MinT - Best Known (120−65, 120, s)-Nets in Base 16

Best Known (120−65, 120, s)-Nets in Base 16

(120−65, 120, 243)-Net over F₁₆ — Constructive and digital

Digital (55, 120, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 120, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(120−65, 120, 281)-Net over F₁₆ — Digital

Digital (55, 120, 281)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−65, 120, 25604)-Net in Base 16 — Upper bound on s

There is no (55, 120, 25605)-net in base 16, because

1 times m-reduction [i] would yield (55, 119, 25605)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 195302 260713 717378 786019 448316 603295 165713 734796 076156 001507 774967 943366 441830 431374 393142 110572 272055 847209 578931 279596 213929 785445 656494 903776 > 16¹¹⁹ [i]