Best Known (87−68, 87, s)-Nets in Base 7
(87−68, 87, 27)-Net over F7 — Constructive and digital
Digital (19, 87, 27)-net over F7, using
- net from sequence [i] based on digital (19, 26)-sequence over F7, using
(87−68, 87, 54)-Net over F7 — Digital
Digital (19, 87, 54)-net over F7, using
- net from sequence [i] based on digital (19, 53)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 19 and N(F) ≥ 54, using
(87−68, 87, 298)-Net in Base 7 — Upper bound on s
There is no (19, 87, 299)-net in base 7, because
- 2 times m-reduction [i] would yield (19, 85, 299)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(785, 299, S7, 66), but
- 1 times code embedding in larger space [i] would yield OA(786, 300, S7, 66), but
- the linear programming bound shows that M ≥ 218 023921 359659 257368 388552 988136 144001 557271 689393 928751 327193 473673 628147 334804 092096 462431 871683 426720 430322 133256 564730 301138 681897 353061 061621 716909 251888 629422 600100 068443 042102 880298 701152 / 33 761283 358366 118574 626890 966711 189878 050649 972940 550333 035043 377324 777020 576330 390888 053448 498989 847143 939996 750005 798715 > 786 [i]
- 1 times code embedding in larger space [i] would yield OA(786, 300, S7, 66), but
- extracting embedded orthogonal array [i] would yield OA(785, 299, S7, 66), but