MinT - Best Known (59, 59+46, s)-Nets in Base 16

Best Known (59, 59+46, s)-Nets in Base 16

(59, 59+46, 526)-Net over F₁₆ — Constructive and digital

Digital (59, 105, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (59, 106, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 53, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(59, 59+46, 781)-Net over F₁₆ — Digital

Digital (59, 105, 781)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+46, 197427)-Net in Base 16 — Upper bound on s

There is no (59, 105, 197428)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 707944 603736 592125 324764 661735 500405 494785 005134 985071 909678 152116 435318 101222 102137 557224 252987 441574 172240 629305 017661 587336 > 16¹⁰⁵ [i]