MinT - Best Known (119−73, 119, s)-Nets in Base 16

Best Known (119−73, 119, s)-Nets in Base 16

(119−73, 119, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 119, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 119, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(119−73, 119, 243)-Net over F₁₆ — Digital

Digital (46, 119, 243)-net over F₁₆, using

net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
  - a curve from the manYPoints database [i]

(119−73, 119, 8403)-Net in Base 16 — Upper bound on s

There is no (46, 119, 8404)-net in base 16, because

1 times m-reduction [i] would yield (46, 118, 8404)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12223 729490 331376 340021 522113 415328 546189 734068 512725 904331 298522 386683 116386 940308 277196 907996 920380 783734 205299 559277 396051 601766 695464 902536 > 16¹¹⁸ [i]