MinT - Best Known (85, 85+36, s)-Nets in Base 5

Best Known (85, 85+36, s)-Nets in Base 5

Digital (85, 121, 296)-net over F₅, using

11 times m-reduction [i] based on digital (85, 132, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 66, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

Digital (85, 121, 925)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹²¹, 925, F₅, 36) (dual of [925, 804, 37]-code), using
- 803 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (8, 4, 2, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 19 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 39 times 0) [i] based on linear OA(5³⁶, 37, F₅, 36) (dual of [37, 1, 37]-code or 37-arc in PG(35,5)), using
  - dual of repetition code with length 37 [i]

There is no (85, 121, 94329)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 762098 728812 012375 596545 589231 229991 813434 005329 131493 736840 451441 692711 111086 386905 > 5¹²¹ [i]