Best Known (78−62, 78, s)-Nets in Base 5
(78−62, 78, 37)-Net over F5 — Constructive and digital
Digital (16, 78, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-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 5 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]
(78−62, 78, 40)-Net over F5 — Digital
Digital (16, 78, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(78−62, 78, 88)-Net in Base 5 — Upper bound on s
There is no (16, 78, 89)-net in base 5, because
- 1 times m-reduction [i] would yield (16, 77, 89)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(577, 89, S5, 61), but
- the linear programming bound shows that M ≥ 16 073029 200579 136053 193829 436480 655203 922651 708126 068115 234375 / 18 485052 > 577 [i]
- extracting embedded orthogonal array [i] would yield OA(577, 89, S5, 61), but