Best Known (7, 7+10, s)-Nets in Base 81
(7, 7+10, 200)-Net over F81 — Constructive and digital
Digital (7, 17, 200)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (1, 11, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81 (see above)
- digital (1, 6, 100)-net over F81, using
(7, 7+10, 306)-Net over F81 — Digital
Digital (7, 17, 306)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8117, 306, F81, 10) (dual of [306, 289, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8117, 328, F81, 10) (dual of [328, 311, 11]-code), using
(7, 7+10, 100365)-Net in Base 81 — Upper bound on s
There is no (7, 17, 100366)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 278 129075 259241 198949 477316 370401 > 8117 [i]