Best Known (12, 12+51, s)-Nets in Base 7
(12, 12+51, 20)-Net over F7 — Constructive and digital
Digital (12, 63, 20)-net over F7, using
- net from sequence [i] based on digital (12, 19)-sequence over F7, using
(12, 12+51, 38)-Net over F7 — Digital
Digital (12, 63, 38)-net over F7, using
- t-expansion [i] based on digital (9, 63, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
(12, 12+51, 165)-Net in Base 7 — Upper bound on s
There is no (12, 63, 166)-net in base 7, because
- 1 times m-reduction [i] would yield (12, 62, 166)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(762, 166, S7, 50), but
- the linear programming bound shows that M ≥ 101 792547 682364 525951 804962 263964 874240 998756 512581 787163 475920 699160 660853 778660 921426 445850 342687 902207 042986 263508 486520 133943 271175 658043 070902 630276 779502 961050 / 4049 531549 017622 947378 237761 681092 013775 698737 547128 420548 551144 374027 650804 875173 331446 608133 184257 018697 865667 > 762 [i]
- extracting embedded orthogonal array [i] would yield OA(762, 166, S7, 50), but