MinT - Best Known (47, 47+58, s)-Nets in Base 16

Best Known (47, 47+58, s)-Nets in Base 16

(47, 47+58, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 105, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 105, 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]

(47, 47+58, 243)-Net over F₁₆ — Digital

Digital (47, 105, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 105, 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]

(47, 47+58, 257)-Net in Base 16

(47, 105, 257)-net in base 16, using

base change [i] based on digital (12, 70, 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]

(47, 47+58, 17798)-Net in Base 16 — Upper bound on s

There is no (47, 105, 17799)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 709237 020434 659530 324328 801534 921804 427206 643046 089286 789666 187726 369192 760629 974209 986062 237645 192426 752838 659076 903595 958816 > 16¹⁰⁵ [i]