MinT - Best Known (69−28, 69, s)-Nets in Base 16

Best Known (69−28, 69, s)-Nets in Base 16

Digital (41, 69, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (41, 70, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 35, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (41, 69, 884)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁶⁹, 884, F₁₆, 28) (dual of [884, 815, 29]-code), using
- 814 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 9 times 0, 1, 10 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 21 times 0, 1, 22 times 0, 1, 26 times 0, 1, 28 times 0, 1, 32 times 0, 1, 35 times 0, 1, 39 times 0, 1, 44 times 0, 1, 49 times 0, 1, 54 times 0, 1, 61 times 0, 1, 67 times 0, 1, 75 times 0, 1, 83 times 0) [i] based on linear OA(16²⁸, 29, F₁₆, 28) (dual of [29, 1, 29]-code or 29-arc in PG(27,16)), using
  - dual of repetition code with length 29 [i]

There is no (41, 69, 346696)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 121418 053898 842014 837403 803367 584841 537427 174947 791813 379328 964602 940389 411978 658136 > 16⁶⁹ [i]