Best Known (9, 9+∞, s)-Nets in Base 25
(9, 9+∞, 104)-Net over F25 — Constructive and digital
Digital (9, m, 104)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
(9, 9+∞, 260)-Net in Base 25 — Upper bound on s
There is no (9, m, 261)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (9, 259, 261)-net in base 25, but
- extracting embedded OOA [i] would yield OA(25259, 261, S25, 250), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 32047 557829 375888 350078 366589 879793 832477 026125 236123 373822 930337 995727 435848 164591 522626 482189 338217 568995 170239 920748 432632 816034 171222 369276 489502 153488 908708 542466 994763 731424 705006 613589 020451 528163 287384 008757 639214 791591 241531 386154 317591 972720 809844 020280 801706 527057 281914 719888 713296 774297 566043 092443 449449 800425 658796 410033 346546 697430 312633 514404 296875 / 251 > 25259 [i]
- extracting embedded OOA [i] would yield OA(25259, 261, S25, 250), but