Best Known (83−64, 83, s)-Nets in Base 7
(83−64, 83, 27)-Net over F7 — Constructive and digital
Digital (19, 83, 27)-net over F7, using
- net from sequence [i] based on digital (19, 26)-sequence over F7, using
(83−64, 83, 54)-Net over F7 — Digital
Digital (19, 83, 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
(83−64, 83, 299)-Net in Base 7 — Upper bound on s
There is no (19, 83, 300)-net in base 7, because
- 4 times m-reduction [i] would yield (19, 79, 300)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(779, 300, S7, 60), but
- the linear programming bound shows that M ≥ 35388 112260 703202 311475 737396 354341 334416 256208 418224 518449 514287 031970 446122 739072 697328 648911 362501 275762 988556 103022 565558 762552 419522 433953 131367 705062 805062 601338 294375 / 4884 775471 756307 491160 745299 208054 021294 151419 575106 728325 087045 981660 876117 357093 549992 399297 754974 474503 > 779 [i]
- extracting embedded orthogonal array [i] would yield OA(779, 300, S7, 60), but