Best Known (12, 34, s)-Nets in Base 3
(12, 34, 20)-Net over F3 — Constructive and digital
Digital (12, 34, 20)-net over F3, using
- t-expansion [i] based on digital (11, 34, 20)-net over F3, using
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 9, N(F) = 19, and 1 place with degree 3 [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
(12, 34, 22)-Net over F3 — Digital
Digital (12, 34, 22)-net over F3, using
- net from sequence [i] based on digital (12, 21)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 12 and N(F) ≥ 22, using
(12, 34, 63)-Net in Base 3 — Upper bound on s
There is no (12, 34, 64)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 18459 398067 921153 > 334 [i]
- extracting embedded orthogonal array [i] would yield OA(334, 64, S3, 22), but
- the linear programming bound shows that M ≥ 14 111105 234476 582146 780186 612485 543683 142605 088372 524627 579947 507340 583313 / 837 608500 983525 185318 819414 283441 298949 343873 086193 807233 > 334 [i]