MinT - Best Known (9, 9+12, s)-Nets in Base 32

Best Known (9, 9+12, s)-Nets in Base 32

Digital (9, 21, 104)-net over F₃₂, using

Digital (9, 21, 125)-net over F₃₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(32²¹, 125, F₃₂, 12) (dual of [125, 104, 13]-code), using
- 38 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 0, 1, 9 times 0, 1, 25 times 0) [i] based on linear OA(32¹⁷, 83, F₃₂, 12) (dual of [83, 66, 13]-code), using
  - extended algebraic-geometric code AG_e(F,70P) [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 83, using
    - a curve from the manYPoints database [i]

(9, 21, 258)-net in base 32, using

base change [i] based on (3, 15, 258)-net in base 128, using
- 1 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
  - base change [i] based on digital (1, 14, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(9, 21, 289)-net in base 32, using

There is no (9, 21, 17899)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 40 569752 733817 404957 936907 586890 > 32²¹ [i]