Best Known (122−27, 122, s)-Nets in Base 5
(122−27, 122, 504)-Net over F5 — Constructive and digital
Digital (95, 122, 504)-net over F5, using
- 52 times duplication [i] based on digital (93, 120, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (33, 46, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 23, 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, 23, 126)-net over F25, using
- digital (47, 74, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 37, 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, 37, 126)-net over F25, using
- digital (33, 46, 252)-net over F5, using
- (u, u+v)-construction [i] based on
(122−27, 122, 5037)-Net over F5 — Digital
Digital (95, 122, 5037)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5122, 5037, F5, 27) (dual of [5037, 4915, 28]-code), using
- 4914 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 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, 6 times 0, 1, 5 times 0, 1, 7 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, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 48 times 0, 1, 52 times 0, 1, 54 times 0, 1, 59 times 0, 1, 62 times 0, 1, 66 times 0, 1, 71 times 0, 1, 75 times 0, 1, 80 times 0, 1, 86 times 0, 1, 91 times 0, 1, 97 times 0, 1, 103 times 0, 1, 110 times 0, 1, 117 times 0, 1, 125 times 0, 1, 133 times 0, 1, 141 times 0, 1, 151 times 0, 1, 160 times 0, 1, 171 times 0, 1, 182 times 0, 1, 193 times 0, 1, 206 times 0, 1, 219 times 0, 1, 234 times 0, 1, 248 times 0, 1, 264 times 0, 1, 282 times 0, 1, 300 times 0) [i] based on linear OA(527, 28, F5, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,5)), using
- dual of repetition code with length 28 [i]
- 4914 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 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, 6 times 0, 1, 5 times 0, 1, 7 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, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 48 times 0, 1, 52 times 0, 1, 54 times 0, 1, 59 times 0, 1, 62 times 0, 1, 66 times 0, 1, 71 times 0, 1, 75 times 0, 1, 80 times 0, 1, 86 times 0, 1, 91 times 0, 1, 97 times 0, 1, 103 times 0, 1, 110 times 0, 1, 117 times 0, 1, 125 times 0, 1, 133 times 0, 1, 141 times 0, 1, 151 times 0, 1, 160 times 0, 1, 171 times 0, 1, 182 times 0, 1, 193 times 0, 1, 206 times 0, 1, 219 times 0, 1, 234 times 0, 1, 248 times 0, 1, 264 times 0, 1, 282 times 0, 1, 300 times 0) [i] based on linear OA(527, 28, F5, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,5)), using
(122−27, 122, 4540911)-Net in Base 5 — Upper bound on s
There is no (95, 122, 4540912)-net in base 5, because
- 1 times m-reduction [i] would yield (95, 121, 4540912)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 3 761587 640384 984632 269583 286654 317029 197140 466868 503192 513175 248877 524347 622196 197825 > 5121 [i]