MinT - Best Known (20, 20+14, s)-Nets in Base 16

Best Known (20, 20+14, s)-Nets in Base 16

Digital (20, 34, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 17, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

Digital (20, 34, 655)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16³⁴, 655, F₁₆, 14) (dual of [655, 621, 15]-code), using
- 11 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 10 times 0) [i] based on linear OA(16³², 642, F₁₆, 14) (dual of [642, 610, 15]-code), using
  - trace code [i] based on linear OA(256¹⁶, 321, F₂₅₆, 14) (dual of [321, 305, 15]-code), using
    - extended algebraic-geometric code AG_e(F,306P) [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 (20, 34, 159002)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 87114 945046 055575 095393 630425 874954 925636 > 16³⁴ [i]