MinT - Best Known (26, 26+17, s)-Nets in Base 16

Best Known (26, 26+17, s)-Nets in Base 16

Digital (26, 43, 538)-net over F₁₆, using

Digital (26, 43, 797)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁴³, 797, F₁₆, 17) (dual of [797, 754, 18]-code), using
- 150 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 0, 0, 1, 11 times 0, 1, 40 times 0, 1, 93 times 0) [i] based on linear OA(16³⁸, 642, F₁₆, 17) (dual of [642, 604, 18]-code), using
  - trace code [i] based on linear OA(256¹⁹, 321, F₂₅₆, 17) (dual of [321, 302, 18]-code), using
    - extended algebraic-geometric code AG_e(F,303P) [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 (26, 43, 526291)-net in base 16, because

1 times m-reduction [i] would yield (26, 42, 526291)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 374 148252 902827 359177 057710 566594 744335 793390 093846 > 16⁴² [i]