MinT - Best Known (17, 17+11, s)-Nets in Base 16

Best Known (17, 17+11, s)-Nets in Base 16

Digital (17, 28, 538)-net over F₁₆, using

Digital (17, 28, 740)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16²⁸, 740, F₁₆, 11) (dual of [740, 712, 12]-code), using
- 158 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 8 times 0, 1, 38 times 0, 1, 109 times 0) [i] based on linear OA(16²⁴, 578, F₁₆, 11) (dual of [578, 554, 12]-code), using
  - trace code [i] based on linear OA(256¹², 289, F₂₅₆, 11) (dual of [289, 277, 12]-code), using
    - extended algebraic-geometric code AG_e(F,277P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

There is no (17, 28, 552067)-net in base 16, because

1 times m-reduction [i] would yield (17, 27, 552067)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 324 521269 373823 036729 147734 771776 > 16²⁷ [i]