Best Known (99−70, 99, s)-Nets in Base 5
(99−70, 99, 51)-Net over F5 — Constructive and digital
Digital (29, 99, 51)-net over F5, using
- t-expansion [i] based on digital (22, 99, 51)-net over F5, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
(99−70, 99, 56)-Net over F5 — Digital
Digital (29, 99, 56)-net over F5, using
- net from sequence [i] based on digital (29, 55)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 29 and N(F) ≥ 56, using
(99−70, 99, 298)-Net in Base 5 — Upper bound on s
There is no (29, 99, 299)-net in base 5, because
- 1 times m-reduction [i] would yield (29, 98, 299)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(598, 299, S5, 69), but
- 1 times code embedding in larger space [i] would yield OA(599, 300, S5, 69), but
- the linear programming bound shows that M ≥ 695 287988 126618 868852 612000 239496 562563 824063 906030 186819 600099 435489 031537 925448 460495 281082 812221 197984 683726 297336 397236 619972 686626 905656 094040 520030 070391 154018 542845 260952 844910 207204 520702 362060 546875 / 280439 373894 412081 020922 879411 708845 744810 893978 969409 355090 253911 885990 228102 657601 796451 470918 711542 266337 280307 291979 665058 394812 540747 > 599 [i]
- 1 times code embedding in larger space [i] would yield OA(599, 300, S5, 69), but
- extracting embedded orthogonal array [i] would yield OA(598, 299, S5, 69), but