MinT - Best Known (53, 53+40, s)-Nets in Base 16

Best Known (53, 53+40, s)-Nets in Base 16

Digital (53, 93, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (53, 94, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 47, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (53, 93, 784)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁹³, 784, F₁₆, 40) (dual of [784, 691, 41]-code), using
- 133 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 37 times 0, 1, 48 times 0) [i] based on linear OA(16⁸⁴, 642, F₁₆, 40) (dual of [642, 558, 41]-code), using
  - trace code [i] based on linear OA(256⁴², 321, F₂₅₆, 40) (dual of [321, 279, 41]-code), using
    - extended algebraic-geometric code AG_e(F,280P) [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 (53, 93, 219964)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9619 677339 555865 199211 667762 260313 695573 334409 163985 903159 295094 611638 333200 663611 433866 570483 016074 916721 524826 > 16⁹³ [i]