Best Known (20−8, 20, s)-Nets in Base 9
(20−8, 20, 232)-Net over F9 — Constructive and digital
Digital (12, 20, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 10, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
(20−8, 20, 239)-Net over F9 — Digital
Digital (12, 20, 239)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(920, 239, F9, 8) (dual of [239, 219, 9]-code), using
- 37 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 30 times 0) [i] based on linear OA(918, 200, F9, 8) (dual of [200, 182, 9]-code), using
- trace code [i] based on linear OA(819, 100, F81, 8) (dual of [100, 91, 9]-code), using
- extended algebraic-geometric code AGe(F,91P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- trace code [i] based on linear OA(819, 100, F81, 8) (dual of [100, 91, 9]-code), using
- 37 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 30 times 0) [i] based on linear OA(918, 200, F9, 8) (dual of [200, 182, 9]-code), using
(20−8, 20, 16335)-Net in Base 9 — Upper bound on s
There is no (12, 20, 16336)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 12 160299 279996 638721 > 920 [i]