Best Known (54−39, 54, s)-Nets in Base 5
(54−39, 54, 36)-Net over F5 — Constructive and digital
Digital (15, 54, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 4 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(54−39, 54, 39)-Net over F5 — Digital
Digital (15, 54, 39)-net over F5, using
- t-expansion [i] based on digital (14, 54, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(54−39, 54, 156)-Net in Base 5 — Upper bound on s
There is no (15, 54, 157)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(554, 157, S5, 39), but
- the linear programming bound shows that M ≥ 278713 627224 633547 271796 867438 967703 332332 899627 718537 583932 629786 431789 398193 359375 000000 / 4866 358615 630033 040600 091027 258825 202934 788811 083799 > 554 [i]