Best Known (51−44, 51, s)-Nets in Base 81
(51−44, 51, 172)-Net over F81 — Constructive and digital
Digital (7, 51, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
(51−44, 51, 190)-Net over F81 — Digital
Digital (7, 51, 190)-net over F81, using
- t-expansion [i] based on digital (6, 51, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(51−44, 51, 2995)-Net in Base 81 — Upper bound on s
There is no (7, 51, 2996)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 21 647574 530391 516400 945106 886355 249501 889760 357306 755270 069852 763453 247550 234093 354039 409919 423361 > 8151 [i]