Best Known (13, 13+42, s)-Nets in Base 5
(13, 13+42, 34)-Net over F5 — Constructive and digital
Digital (13, 55, 34)-net over F5, using
- net from sequence [i] based on digital (13, 33)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 2 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(13, 13+42, 36)-Net over F5 — Digital
Digital (13, 55, 36)-net over F5, using
- net from sequence [i] based on digital (13, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 13 and N(F) ≥ 36, using
(13, 13+42, 110)-Net in Base 5 — Upper bound on s
There is no (13, 55, 111)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(555, 111, S5, 42), but
- the linear programming bound shows that M ≥ 160853 279936 737552 555198 128869 197813 289096 417064 664252 625210 703762 775947 531935 988567 594340 303445 331728 542422 687140 745313 253093 155785 813453 223742 630626 702521 112747 490406 036376 953125 / 536 589983 881878 199097 989987 030752 034222 690321 138323 583380 431752 510971 338373 024133 973551 937142 609922 974314 325056 884114 362477 705400 313499 352891 > 555 [i]