Best Known (81, 81+62, s)-Nets in Base 8
(81, 81+62, 354)-Net over F8 — Constructive and digital
Digital (81, 143, 354)-net over F8, using
- 5 times m-reduction [i] based on digital (81, 148, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 74, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 74, 177)-net over F64, using
(81, 81+62, 425)-Net over F8 — Digital
Digital (81, 143, 425)-net over F8, using
(81, 81+62, 25970)-Net in Base 8 — Upper bound on s
There is no (81, 143, 25971)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1387 496287 889354 677952 690811 450414 114354 828143 934954 657401 443565 437469 772418 078955 739814 792278 125114 930081 822636 832609 709887 672672 > 8143 [i]