Best Known (22, 46, s)-Nets in Base 81
(22, 46, 370)-Net over F81 — Constructive and digital
Digital (22, 46, 370)-net over F81, using
- t-expansion [i] based on digital (16, 46, 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
(22, 46, 897)-Net over F81 — Digital
Digital (22, 46, 897)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8146, 897, F81, 24) (dual of [897, 851, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 1312, F81, 24) (dual of [1312, 1266, 25]-code), using
(22, 46, 1368134)-Net in Base 81 — Upper bound on s
There is no (22, 46, 1368135)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 6170 379012 941481 513083 352922 169791 617585 249264 855879 607622 207120 133877 885022 937824 641601 > 8146 [i]