MinT - Best Known (36, 61, s)-Nets in Base 16

Best Known (36, 61, s)-Nets in Base 16

Digital (36, 61, 524)-net over F₁₆, using

1 times m-reduction [i] based on digital (36, 62, 524)-net over F₁₆, using
- trace code for nets [i] based on digital (5, 31, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (36, 61, 770)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁶¹, 770, F₁₆, 25) (dual of [770, 709, 26]-code), using
- 121 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 0, 1, 6 times 0, 1, 15 times 0, 1, 34 times 0, 1, 60 times 0) [i] based on linear OA(16⁵⁴, 642, F₁₆, 25) (dual of [642, 588, 26]-code), using
  - trace code [i] based on linear OA(256²⁷, 321, F₂₅₆, 25) (dual of [321, 294, 26]-code), using
    - extended algebraic-geometric code AG_e(F,295P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

There is no (36, 61, 369712)-net in base 16, because

1 times m-reduction [i] would yield (36, 60, 369712)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 766890 002810 686676 032036 142856 323306 255296 343806 139405 047439 055335 720211 > 16⁶⁰ [i]