MinT - Best Known (62, 86, s)-Nets in Base 5

Best Known (62, 86, s)-Nets in Base 5

Digital (62, 86, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 43, 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 (62, 86, 980)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁸⁶, 980, F₅, 24) (dual of [980, 894, 25]-code), using
- 893 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 29 times 0, 1, 30 times 0, 1, 33 times 0, 1, 36 times 0, 1, 38 times 0, 1, 41 times 0, 1, 44 times 0, 1, 47 times 0, 1, 51 times 0, 1, 55 times 0, 1, 59 times 0, 1, 64 times 0) [i] based on linear OA(5²⁴, 25, F₅, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,5)), using
  - dual of repetition code with length 25 [i]

There is no (62, 86, 135071)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 292576 504098 964058 097575 225971 090599 499381 426433 192892 193745 > 5⁸⁶ [i]