MinT - Best Known (108−60, 108, s)-Nets in Base 16

Best Known (108−60, 108, s)-Nets in Base 16

(108−60, 108, 243)-Net over F₁₆ — Constructive and digital

Digital (48, 108, 243)-net over F₁₆, using

net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
  - a function field by GarcÃa and Quoos [i]

(108−60, 108, 257)-Net in Base 16

(48, 108, 257)-net in base 16, using

base change [i] based on digital (12, 72, 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]

(108−60, 108, 17342)-Net in Base 16 — Upper bound on s

There is no (48, 108, 17343)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11096 630016 296529 105138 817403 922611 398411 603428 010218 483408 480877 598819 672141 577002 762906 573033 040379 356144 435413 392304 252288 237851 > 16¹⁰⁸ [i]