MinT - Best Known (128−110, 128, s)-Nets in Base 16

Best Known (128−110, 128, s)-Nets in Base 16

(128−110, 128, 65)-Net over F₁₆ — Constructive and digital

Digital (18, 128, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 128, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(128−110, 128, 113)-Net over F₁₆ — Digital

Digital (18, 128, 113)-net over F₁₆, using

net from sequence [i] based on digital (18, 112)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 18 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(128−110, 128, 871)-Net in Base 16 — Upper bound on s

There is no (18, 128, 872)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13446 840952 776833 271765 835649 864126 074495 054058 701988 827598 576302 295968 510504 143322 621420 316965 898424 424540 296664 357726 461324 820450 565746 439338 061849 194276 > 16¹²⁸ [i]