MinT - Best Known (49, 49+38, s)-Nets in Base 16

Best Known (49, 49+38, s)-Nets in Base 16

Digital (49, 87, 524)-net over F₁₆, using

1 times m-reduction [i] based on digital (49, 88, 524)-net over F₁₆, using
- trace code for nets [i] based on digital (5, 44, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (49, 87, 696)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁸⁷, 696, F₁₆, 38) (dual of [696, 609, 39]-code), using
- 47 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 25 times 0) [i] based on linear OA(16⁸⁰, 642, F₁₆, 38) (dual of [642, 562, 39]-code), using
  - trace code [i] based on linear OA(256⁴⁰, 321, F₂₅₆, 38) (dual of [321, 281, 39]-code), using
    - extended algebraic-geometric code AG_e(F,282P) [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 (49, 87, 172465)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 573 388488 904646 250554 707326 283893 604818 256838 618537 660384 986641 158100 704879 944083 334676 202675 815237 015776 > 16⁸⁷ [i]