Best Known (99−83, 99, s)-Nets in Base 9
(99−83, 99, 64)-Net over F9 — Constructive and digital
Digital (16, 99, 64)-net over F9, using
- t-expansion [i] based on digital (13, 99, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
(99−83, 99, 74)-Net over F9 — Digital
Digital (16, 99, 74)-net over F9, using
- net from sequence [i] based on digital (16, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 16 and N(F) ≥ 74, using
(99−83, 99, 299)-Net in Base 9 — Upper bound on s
There is no (16, 99, 300)-net in base 9, because
- 7 times m-reduction [i] would yield (16, 92, 300)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(992, 300, S9, 76), but
- the linear programming bound shows that M ≥ 9890 568638 574786 675103 460511 863747 895995 272845 962887 362514 930557 142728 145142 062221 183632 543259 091889 611584 309772 925111 106036 259180 480144 964622 355994 233872 694494 361703 427784 450281 868057 510605 217730 819644 999561 446056 683535 309555 134064 937718 264748 534249 289843 750000 / 1 242537 630150 507386 574099 797362 035795 465040 968205 569767 404834 009775 840703 341696 609520 398082 085187 611449 502829 470519 542017 742852 478521 772776 927787 466519 251204 103277 669767 878193 > 992 [i]
- extracting embedded orthogonal array [i] would yield OA(992, 300, S9, 76), but