Best Known (13, 97, s)-Nets in Base 9
(13, 97, 64)-Net over F9 — Constructive and digital
Digital (13, 97, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
(13, 97, 284)-Net over F9 — Upper bound on s (digital)
There is no digital (13, 97, 285)-net over F9, because
- 3 times m-reduction [i] would yield digital (13, 94, 285)-net over F9, but
- extracting embedded orthogonal array [i] would yield linear OA(994, 285, F9, 81) (dual of [285, 191, 82]-code), but
- residual code [i] would yield OA(913, 203, S9, 9), but
- 1 times truncation [i] would yield OA(912, 202, S9, 8), but
- the linear programming bound shows that M ≥ 6 065486 598426 741486 / 21 034639 > 912 [i]
- 1 times truncation [i] would yield OA(912, 202, S9, 8), but
- residual code [i] would yield OA(913, 203, S9, 9), but
- extracting embedded orthogonal array [i] would yield linear OA(994, 285, F9, 81) (dual of [285, 191, 82]-code), but
(13, 97, 286)-Net in Base 9 — Upper bound on s
There is no (13, 97, 287)-net in base 9, because
- 31 times m-reduction [i] would yield (13, 66, 287)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(966, 287, S9, 53), but
- the linear programming bound shows that M ≥ 4 701185 910622 895400 692972 864147 915182 309494 400566 046227 107459 723312 543397 223585 106747 703482 267203 702093 832310 441601 420674 771422 961528 459375 / 4501 341323 225343 451656 715832 334722 302456 067665 665734 100769 909721 334710 622719 > 966 [i]
- extracting embedded orthogonal array [i] would yield OA(966, 287, S9, 53), but