Best Known (7, 16, s)-Nets in Base 81
(7, 16, 246)-Net over F81 — Constructive and digital
Digital (7, 16, 246)-net over F81, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 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 (0, 4, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 9, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 3, 82)-net over F81, using
(7, 16, 350)-Net over F81 — Digital
Digital (7, 16, 350)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8116, 350, F81, 9) (dual of [350, 334, 10]-code), using
(7, 16, 396990)-Net in Base 81 — Upper bound on s
There is no (7, 16, 396991)-net in base 81, because
- 1 times m-reduction [i] would yield (7, 15, 396991)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 42391 436499 640703 903952 547521 > 8115 [i]