Best Known (20, 28, s)-Nets in Base 9
(20, 28, 492)-Net over F9 — Constructive and digital
Digital (20, 28, 492)-net over F9, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 4, 164)-net over F9, using
- s-reduction based on digital (2, 4, 820)-net over F9, using
- digital (4, 8, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 4, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 4, 82)-net over F81, using
- digital (8, 16, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 8, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- trace code for nets [i] based on digital (0, 8, 82)-net over F81, using
- digital (2, 4, 164)-net over F9, using
(20, 28, 2776)-Net over F9 — Digital
Digital (20, 28, 2776)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(928, 2776, F9, 8) (dual of [2776, 2748, 9]-code), using
- 2746 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 7 times 0, 1, 10 times 0, 1, 16 times 0, 1, 21 times 0, 1, 31 times 0, 1, 42 times 0, 1, 59 times 0, 1, 81 times 0, 1, 111 times 0, 1, 153 times 0, 1, 211 times 0, 1, 289 times 0, 1, 397 times 0, 1, 544 times 0, 1, 745 times 0) [i] based on linear OA(98, 10, F9, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
- extended Reed–Solomon code RSe(2,9) [i]
- Simplex code S(2,9) [i]
- 2746 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 7 times 0, 1, 10 times 0, 1, 16 times 0, 1, 21 times 0, 1, 31 times 0, 1, 42 times 0, 1, 59 times 0, 1, 81 times 0, 1, 111 times 0, 1, 153 times 0, 1, 211 times 0, 1, 289 times 0, 1, 397 times 0, 1, 544 times 0, 1, 745 times 0) [i] based on linear OA(98, 10, F9, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
(20, 28, 1323304)-Net in Base 9 — Upper bound on s
There is no (20, 28, 1323305)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 523 348694 987479 983638 415521 > 928 [i]