MinT - Best Known (129−86, 129, s)-Nets in Base 16

Best Known (129−86, 129, s)-Nets in Base 16

(129−86, 129, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 129, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 129, 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]

(129−86, 129, 226)-Net over F₁₆ — Digital

Digital (43, 129, 226)-net over F₁₆, using

net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
  - Drinfeld modules of rank 1 [i]

(129−86, 129, 4586)-Net in Base 16 — Upper bound on s

There is no (43, 129, 4587)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 215428 848377 794773 264022 371822 350193 492159 788156 296764 161568 802858 472763 240488 666716 837297 332789 119745 562730 630188 109513 166380 277076 286227 175702 824477 656016 > 16¹²⁹ [i]