Best Known (35, 73, s)-Nets in Base 81
(35, 73, 452)-Net over F81 — Constructive and digital
Digital (35, 73, 452)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 19, 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
- digital (16, 54, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- digital (0, 19, 82)-net over F81, using
(35, 73, 1155)-Net over F81 — Digital
Digital (35, 73, 1155)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8173, 1155, F81, 38) (dual of [1155, 1082, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(8173, 1312, F81, 38) (dual of [1312, 1239, 39]-code), using
(35, 73, 2131689)-Net in Base 81 — Upper bound on s
There is no (35, 73, 2131690)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 20 864491 215158 556857 342590 845709 125953 655271 470430 848216 888437 476998 830749 652003 263931 718532 454314 411289 120825 658249 828308 928985 339391 496801 > 8173 [i]