MinT - Best Known (61, 61+22, s)-Nets in Base 5

Best Known (61, 61+22, s)-Nets in Base 5

Digital (61, 83, 296)-net over F₅, using

1 times m-reduction [i] based on digital (61, 84, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 42, 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 (61, 83, 1267)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁸³, 1267, F₅, 22) (dual of [1267, 1184, 23]-code), using
- 1183 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (5, 3, 1, 2, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 30 times 0, 1, 32 times 0, 1, 35 times 0, 1, 38 times 0, 1, 41 times 0, 1, 45 times 0, 1, 48 times 0, 1, 52 times 0, 1, 57 times 0, 1, 61 times 0, 1, 66 times 0, 1, 72 times 0, 1, 77 times 0, 1, 84 times 0, 1, 91 times 0) [i] based on linear OA(5²², 23, F₅, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,5)), using
  - dual of repetition code with length 23 [i]

There is no (61, 83, 230668)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 10340 119051 076574 671695 917968 359377 365435 058120 900650 187569 > 5⁸³ [i]