MinT - Best Known (102−56, 102, s)-Nets in Base 16

Best Known (102−56, 102, s)-Nets in Base 16

(102−56, 102, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 102, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 102, 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]

(102−56, 102, 243)-Net over F₁₆ — Digital

Digital (46, 102, 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]

(102−56, 102, 257)-Net in Base 16

(46, 102, 257)-net in base 16, using

base change [i] based on digital (12, 68, 257)-net over F₆₄, using
- net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(102−56, 102, 18322)-Net in Base 16 — Upper bound on s

There is no (46, 102, 18323)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 661 470584 156443 672060 936845 936671 698937 474542 752909 500046 698335 424714 359698 429552 334528 233843 533397 728007 973657 166276 506336 > 16¹⁰² [i]