Best Known (131−29, 131, s)-Nets in Base 5
(131−29, 131, 504)-Net over F5 — Constructive and digital
Digital (102, 131, 504)-net over F5, using
- t-expansion [i] based on digital (101, 131, 504)-net over F5, using
- 1 times m-reduction [i] based on digital (101, 132, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (35, 50, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 25, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 25, 126)-net over F25, using
- digital (51, 82, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 41, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- trace code for nets [i] based on digital (10, 41, 126)-net over F25, using
- digital (35, 50, 252)-net over F5, using
- (u, u+v)-construction [i] based on
- 1 times m-reduction [i] based on digital (101, 132, 504)-net over F5, using
(131−29, 131, 5276)-Net over F5 — Digital
Digital (102, 131, 5276)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5131, 5276, F5, 29) (dual of [5276, 5145, 30]-code), using
- 5144 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 38 times 0, 1, 39 times 0, 1, 42 times 0, 1, 45 times 0, 1, 48 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0, 1, 60 times 0, 1, 64 times 0, 1, 68 times 0, 1, 72 times 0, 1, 77 times 0, 1, 81 times 0, 1, 86 times 0, 1, 91 times 0, 1, 96 times 0, 1, 103 times 0, 1, 108 times 0, 1, 115 times 0, 1, 122 times 0, 1, 130 times 0, 1, 137 times 0, 1, 146 times 0, 1, 154 times 0, 1, 163 times 0, 1, 173 times 0, 1, 184 times 0, 1, 195 times 0, 1, 206 times 0, 1, 218 times 0, 1, 232 times 0, 1, 245 times 0, 1, 260 times 0, 1, 276 times 0, 1, 292 times 0) [i] based on linear OA(529, 30, F5, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,5)), using
- dual of repetition code with length 30 [i]
- 5144 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 38 times 0, 1, 39 times 0, 1, 42 times 0, 1, 45 times 0, 1, 48 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0, 1, 60 times 0, 1, 64 times 0, 1, 68 times 0, 1, 72 times 0, 1, 77 times 0, 1, 81 times 0, 1, 86 times 0, 1, 91 times 0, 1, 96 times 0, 1, 103 times 0, 1, 108 times 0, 1, 115 times 0, 1, 122 times 0, 1, 130 times 0, 1, 137 times 0, 1, 146 times 0, 1, 154 times 0, 1, 163 times 0, 1, 173 times 0, 1, 184 times 0, 1, 195 times 0, 1, 206 times 0, 1, 218 times 0, 1, 232 times 0, 1, 245 times 0, 1, 260 times 0, 1, 276 times 0, 1, 292 times 0) [i] based on linear OA(529, 30, F5, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,5)), using
(131−29, 131, 4675548)-Net in Base 5 — Upper bound on s
There is no (102, 131, 4675549)-net in base 5, because
- 1 times m-reduction [i] would yield (102, 130, 4675549)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 7 346848 927423 239900 403369 422361 229117 404061 620141 004940 274937 553622 531905 651634 863998 250345 > 5130 [i]