Best Known (64−47, 64, s)-Nets in Base 5
(64−47, 64, 42)-Net over F5 — Constructive and digital
Digital (17, 64, 42)-net over F5, using
- net from sequence [i] based on digital (17, 41)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using
(64−47, 64, 158)-Net in Base 5 — Upper bound on s
There is no (17, 64, 159)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(564, 159, S5, 47), but
- the linear programming bound shows that M ≥ 897407 663252 381419 170129 724984 295994 535437 632347 927430 279538 043008 815855 156284 802160 818674 343700 486905 421804 011025 118429 988668 663043 824835 767736 658453 941345 214843 750000 000000 / 1653 804576 872481 663656 213124 763739 754832 585906 842331 184075 361292 614659 970640 694448 547731 391996 815938 094809 675890 024598 791604 410921 > 564 [i]