MinT - Best Known (60, 60+61, s)-Nets in Base 16

Best Known (60, 60+61, s)-Nets in Base 16

(60, 60+61, 257)-Net over F₁₆ — Constructive and digital

Digital (60, 121, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(60,256) in PG(120,16)) for nets [i] based on digital (0, 61, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(60, 60+61, 403)-Net over F₁₆ — Digital

Digital (60, 121, 403)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+61, 52606)-Net in Base 16 — Upper bound on s

There is no (60, 121, 52607)-net in base 16, because

1 times m-reduction [i] would yield (60, 120, 52607)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 122261 449173 461551 057639 130404 237884 087396 213110 561209 400379 531781 021617 568175 085166 669557 354574 442765 575434 454453 833456 021637 210837 407442 536151 > 16¹²⁰ [i]