MinT - Best Known (85−64, 85, s)-Nets in Base 16

Best Known (85−64, 85, s)-Nets in Base 16

(85−64, 85, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 85, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 85, 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]

(85−64, 85, 129)-Net over F₁₆ — Digital

Digital (21, 85, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 85, 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]

(85−64, 85, 1329)-Net in Base 16 — Upper bound on s

There is no (21, 85, 1330)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 293245 199441 086831 351536 035128 348632 924081 894727 285769 847518 417222 485786 052940 873649 622769 647834 116151 > 16⁸⁵ [i]