Best Known (19, 19+77, s)-Nets in Base 7
(19, 19+77, 27)-Net over F7 — Constructive and digital
Digital (19, 96, 27)-net over F7, using
- net from sequence [i] based on digital (19, 26)-sequence over F7, using
(19, 19+77, 54)-Net over F7 — Digital
Digital (19, 96, 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
(19, 19+77, 297)-Net in Base 7 — Upper bound on s
There is no (19, 96, 298)-net in base 7, because
- 5 times m-reduction [i] would yield (19, 91, 298)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(791, 298, S7, 72), but
- 2 times code embedding in larger space [i] would yield OA(793, 300, S7, 72), but
- the linear programming bound shows that M ≥ 728384 102664 463869 547718 665664 627862 412495 059558 357444 212261 856556 479386 872482 923282 511608 929845 445585 107759 983247 397759 362268 325695 250986 990071 338104 009005 903512 051476 004695 032459 428946 096948 171552 108391 892783 325188 733095 088054 724451 810208 000000 / 147971 862268 209097 126722 220347 755161 647890 710655 411438 128353 310669 205076 890596 319870 047827 172179 911400 512911 825089 867664 506375 310455 210207 145195 926708 884674 858215 688069 > 793 [i]
- 2 times code embedding in larger space [i] would yield OA(793, 300, S7, 72), but
- extracting embedded orthogonal array [i] would yield OA(791, 298, S7, 72), but