MinT - Best Known (41−16, 41, s)-Nets in Base 16

Best Known (41−16, 41, s)-Nets in Base 16

Digital (25, 41, 538)-net over F₁₆, using

Digital (25, 41, 850)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁴¹, 850, F₁₆, 16) (dual of [850, 809, 17]-code), using
- 203 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 4 times 0, 1, 19 times 0, 1, 58 times 0, 1, 118 times 0) [i] based on linear OA(16³⁶, 642, F₁₆, 16) (dual of [642, 606, 17]-code), using
  - trace code [i] based on linear OA(256¹⁸, 321, F₂₅₆, 16) (dual of [321, 303, 17]-code), using
    - extended algebraic-geometric code AG_e(F,304P) [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 (25, 41, 372143)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 23 384389 645340 727618 949660 844685 679335 223097 275711 > 16⁴¹ [i]