Best Known (62, 123, s)-Nets in Base 8
(62, 123, 130)-Net over F8 — Constructive and digital
Digital (62, 123, 130)-net over F8, using
- 1 times m-reduction [i] based on digital (62, 124, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 62, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 62, 65)-net over F64, using
(62, 123, 213)-Net over F8 — Digital
Digital (62, 123, 213)-net over F8, using
(62, 123, 8076)-Net in Base 8 — Upper bound on s
There is no (62, 123, 8077)-net in base 8, because
- 1 times m-reduction [i] would yield (62, 122, 8077)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 150 324481 324323 980959 003283 036516 991420 711299 902651 168131 392513 367156 844085 918017 264336 125097 504701 962716 034112 > 8122 [i]