MinT - Best Known (44, 44+52, s)-Nets in Base 16

Best Known (44, 44+52, s)-Nets in Base 16

(44, 44+52, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 96, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 96, 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]

(44, 44+52, 233)-Net over F₁₆ — Digital

Digital (44, 96, 233)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+52, 257)-Net in Base 16

(44, 96, 257)-net in base 16, using

base change [i] based on digital (12, 64, 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]

(44, 44+52, 19627)-Net in Base 16 — Upper bound on s

There is no (44, 96, 19628)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 419827 551480 698921 016279 730582 726815 407262 953630 991280 716016 102559 968473 867142 312593 685831 907731 351179 917841 828046 > 16⁹⁶ [i]