MinT - Best Known (46−18, 46, s)-Nets in Base 16

Best Known (46−18, 46, s)-Nets in Base 16

Digital (28, 46, 538)-net over F₁₆, using

Digital (28, 46, 877)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁴⁶, 877, F₁₆, 18) (dual of [877, 831, 19]-code), using
- 291 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 0, 0, 1, 8 times 0, 1, 21 times 0, 1, 48 times 0, 1, 85 times 0, 1, 121 times 0) [i] based on linear OA(16³⁸, 578, F₁₆, 18) (dual of [578, 540, 19]-code), using
  - trace code [i] based on linear OA(256¹⁹, 289, F₂₅₆, 18) (dual of [289, 270, 19]-code), using
    - extended algebraic-geometric code AG_e(F,270P) [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 (28, 46, 394500)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 24 520365 657660 137810 116312 313132 372938 707501 595550 529376 > 16⁴⁶ [i]