Best Known (66−55, 66, s)-Nets in Base 8
(66−55, 66, 48)-Net over F8 — Constructive and digital
Digital (11, 66, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
(66−55, 66, 186)-Net in Base 8 — Upper bound on s
There is no (11, 66, 187)-net in base 8, because
- 4 times m-reduction [i] would yield (11, 62, 187)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(862, 187, S8, 51), but
- the linear programming bound shows that M ≥ 486 077877 347552 688790 679815 507810 642176 594417 217572 526710 667826 470675 232790 901201 089388 680444 610709 329460 005247 500938 816258 220851 345374 576640 / 4 837688 162429 564662 522847 813829 015730 651336 054402 266904 729358 109884 366756 784267 489073 > 862 [i]
- extracting embedded orthogonal array [i] would yield OA(862, 187, S8, 51), but