Best Known (91−57, 91, s)-Nets in Base 4
(91−57, 91, 56)-Net over F4 — Constructive and digital
Digital (34, 91, 56)-net over F4, using
- t-expansion [i] based on digital (33, 91, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(91−57, 91, 65)-Net over F4 — Digital
Digital (34, 91, 65)-net over F4, using
- t-expansion [i] based on digital (33, 91, 65)-net over F4, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 65, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
(91−57, 91, 299)-Net in Base 4 — Upper bound on s
There is no (34, 91, 300)-net in base 4, because
- 1 times m-reduction [i] would yield (34, 90, 300)-net in base 4, but
- extracting embedded orthogonal array [i] would yield OA(490, 300, S4, 56), but
- the linear programming bound shows that M ≥ 436432 663383 056419 717825 118031 037669 695806 931459 228146 549597 109866 228835 207497 684949 420603 397716 437702 445220 085958 062968 094084 353631 453184 / 252220 182913 707539 004210 070528 097549 966949 311513 543692 315598 955307 835461 085957 375101 > 490 [i]
- extracting embedded orthogonal array [i] would yield OA(490, 300, S4, 56), but