Best Known (38, 82, s)-Nets in Base 9
(38, 82, 92)-Net over F9 — Constructive and digital
Digital (38, 82, 92)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 25, 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 (13, 57, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (3, 25, 28)-net over F9, using
(38, 82, 94)-Net in Base 9 — Constructive
(38, 82, 94)-net in base 9, using
- 2 times m-reduction [i] based on (38, 84, 94)-net in base 9, using
- base change [i] based on digital (10, 56, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- base change [i] based on digital (10, 56, 94)-net over F27, using
(38, 82, 129)-Net over F9 — Digital
Digital (38, 82, 129)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(982, 129, F9, 3, 44) (dual of [(129, 3), 305, 45]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(982, 130, F9, 3, 44) (dual of [(130, 3), 308, 45]-NRT-code), using
- strength reduction [i] based on linear OOA(982, 130, F9, 3, 45) (dual of [(130, 3), 308, 46]-NRT-code), using
- construction X applied to AG(3;F,335P) ⊂ AG(3;F,340P) [i] based on
- linear OOA(978, 127, F9, 3, 45) (dual of [(127, 3), 303, 46]-NRT-code), using algebraic-geometric NRT-code AG(3;F,335P) [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
- linear OOA(973, 127, F9, 3, 40) (dual of [(127, 3), 308, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,340P) [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128 (see above)
- linear OOA(94, 3, F9, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(94, 9, F9, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
- Reed–Solomon NRT-code RS(3;23,9) [i]
- discarding factors / shortening the dual code based on linear OOA(94, 9, F9, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
- construction X applied to AG(3;F,335P) ⊂ AG(3;F,340P) [i] based on
- strength reduction [i] based on linear OOA(982, 130, F9, 3, 45) (dual of [(130, 3), 308, 46]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(982, 130, F9, 3, 44) (dual of [(130, 3), 308, 45]-NRT-code), using
(38, 82, 4065)-Net in Base 9 — Upper bound on s
There is no (38, 82, 4066)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 778074 856319 513908 803633 342759 846312 027385 850211 559608 408597 267462 933841 026209 > 982 [i]