Best Known (35−23, 35, s)-Nets in Base 3
(35−23, 35, 20)-Net over F3 — Constructive and digital
Digital (12, 35, 20)-net over F3, using
- t-expansion [i] based on digital (11, 35, 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
(35−23, 35, 22)-Net over F3 — Digital
Digital (12, 35, 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
(35−23, 35, 58)-Net in Base 3 — Upper bound on s
There is no (12, 35, 59)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(335, 59, S3, 23), but
- the linear programming bound shows that M ≥ 11 881571 752387 686082 840889 250973 610314 209645 / 220 540905 770086 735386 705152 > 335 [i]