MinT - Best Known (21, 129, s)-Nets in Base 16

Best Known (21, 129, s)-Nets in Base 16

(21, 129, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 129, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 129, 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]

(21, 129, 129)-Net over F₁₆ — Digital

Digital (21, 129, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 129, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(21, 129, 1021)-Net in Base 16 — Upper bound on s

There is no (21, 129, 1022)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 214781 894792 980020 509614 530140 350144 214630 880835 283757 931876 780756 202478 626647 430629 012583 363996 438368 795054 906051 413880 639291 543394 316304 705638 525722 848996 > 16¹²⁹ [i]