Best Known (45−40, 45, s)-Nets in Base 81
(45−40, 45, 160)-Net over F81 — Constructive and digital
Digital (5, 45, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
(45−40, 45, 167)-Net over F81 — Digital
Digital (5, 45, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
(45−40, 45, 2033)-Net in Base 81 — Upper bound on s
There is no (5, 45, 2034)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 76 593332 474458 188276 201262 304513 534074 807247 194038 120902 105627 080500 182358 493232 374401 > 8145 [i]