Best Known (18, 18+29, s)-Nets in Base 3
(18, 18+29, 28)-Net over F3 — Constructive and digital
Digital (18, 47, 28)-net over F3, using
- t-expansion [i] based on digital (15, 47, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
(18, 18+29, 97)-Net in Base 3 — Upper bound on s
There is no (18, 47, 98)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(347, 98, S3, 29), but
- the linear programming bound shows that M ≥ 878 477050 399465 980453 586964 621683 950945 825552 118293 117602 606940 452170 734253 585262 297198 473545 761020 539044 338608 428856 029736 435218 060473 114456 457998 924129 518360 / 30199 974942 421513 556360 479891 280022 754509 642755 016668 779791 476632 116780 160390 870401 269944 342867 928383 288956 335499 173579 071230 927447 031903 > 347 [i]