MinT - Best Known (89−85, 89, s)-Nets in Base 25

Best Known (89−85, 89, s)-Nets in Base 25

(89−85, 89, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 89, 66)-net over F₂₅, using

net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]

(89−85, 89, 262)-Net in Base 25 — Upper bound on s

There is no (4, 89, 263)-net in base 25, because

3 times m-reduction [i] would yield (4, 86, 263)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(25⁸⁶, 263, S₂₅, 82), but
  - the linear programming bound shows that MÂ â‰¥ 124838 157887 948575 069973 603564 217894 140049 811879 259470 500094 671199 192064 814369 803279 087877 393316 825789 390511 262347 445431 419856 731736 217625 439167 022705 078125 / 73787 952480 415645 668068 103685 901541 > 25⁸⁶ [i]