Best Known (73−24, 73, s)-Nets in Base 9
(73−24, 73, 348)-Net over F9 — Constructive and digital
Digital (49, 73, 348)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (34, 58, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 29, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 29, 160)-net over F81, using
- digital (3, 15, 28)-net over F9, using
(73−24, 73, 1271)-Net over F9 — Digital
Digital (49, 73, 1271)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(973, 1271, F9, 24) (dual of [1271, 1198, 25]-code), using
- 1197 step Varšamov–Edel lengthening with (ri) = (4, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 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, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 8 times 0, 1, 8 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 28 times 0, 1, 31 times 0, 1, 35 times 0, 1, 38 times 0, 1, 42 times 0, 1, 46 times 0, 1, 52 times 0, 1, 57 times 0, 1, 62 times 0, 1, 69 times 0, 1, 77 times 0, 1, 84 times 0, 1, 93 times 0, 1, 102 times 0, 1, 113 times 0) [i] based on linear OA(924, 25, F9, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,9)), using
- dual of repetition code with length 25 [i]
- 1197 step Varšamov–Edel lengthening with (ri) = (4, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 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, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 8 times 0, 1, 8 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 28 times 0, 1, 31 times 0, 1, 35 times 0, 1, 38 times 0, 1, 42 times 0, 1, 46 times 0, 1, 52 times 0, 1, 57 times 0, 1, 62 times 0, 1, 69 times 0, 1, 77 times 0, 1, 84 times 0, 1, 93 times 0, 1, 102 times 0, 1, 113 times 0) [i] based on linear OA(924, 25, F9, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,9)), using
(73−24, 73, 421929)-Net in Base 9 — Upper bound on s
There is no (49, 73, 421930)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4567 874965 560256 393573 511021 032167 846643 104303 366838 791474 310115 504961 > 973 [i]