Best Known (9, ∞, s)-Nets in Base 27
(9, ∞, 88)-Net over F27 — Constructive and digital
Digital (9, m, 88)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
(9, ∞, 99)-Net over F27 — Digital
Digital (9, m, 99)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (9, 98)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 99, using
(9, ∞, 280)-Net in Base 27 — Upper bound on s
There is no (9, m, 281)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (9, 279, 281)-net in base 27, but
- extracting embedded OOA [i] would yield OA(27279, 281, S27, 270), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 665651 093336 585887 663390 454601 762573 636924 262941 933583 189097 177586 265214 049566 469425 886480 800406 475831 694836 426814 691517 607095 408308 244688 335370 669511 799703 648393 644354 185105 224149 839300 682041 340185 177211 315293 456088 734878 496557 943986 954406 782428 700449 440292 838949 627724 086402 262861 983740 747671 395752 182687 193862 194905 472619 479019 490720 975315 983898 409817 777649 415735 725276 193213 484560 227272 927916 952811 / 271 > 27279 [i]
- extracting embedded OOA [i] would yield OA(27279, 281, S27, 270), but