MinT - Best Known (41, 41+30, s)-Nets in Base 16

Best Known (41, 41+30, s)-Nets in Base 16

Digital (41, 71, 524)-net over F₁₆, using

1 times m-reduction [i] based on digital (41, 72, 524)-net over F₁₆, using
- trace code for nets [i] based on digital (5, 36, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (41, 71, 717)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁷¹, 717, F₁₆, 30) (dual of [717, 646, 31]-code), using
- 68 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 1, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 37 times 0) [i] based on linear OA(16⁶⁴, 642, F₁₆, 30) (dual of [642, 578, 31]-code), using
  - trace code [i] based on linear OA(256³², 321, F₂₅₆, 30) (dual of [321, 289, 31]-code), using
    - extended algebraic-geometric code AG_e(F,290P) [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 (41, 71, 214369)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 31 084372 790641 041903 092167 610684 495591 002712 036122 536481 303995 759831 930125 864012 471776 > 16⁷¹ [i]