Best Known (65, 128, s)-Nets in Base 8
(65, 128, 160)-Net over F8 — Constructive and digital
Digital (65, 128, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 64, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(65, 128, 227)-Net over F8 — Digital
Digital (65, 128, 227)-net over F8, using
(65, 128, 8866)-Net in Base 8 — Upper bound on s
There is no (65, 128, 8867)-net in base 8, because
- 1 times m-reduction [i] would yield (65, 127, 8867)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 4 937903 673965 569341 581191 851130 459176 781625 406196 882428 322164 887560 208107 040469 555731 274683 688274 812560 646453 024480 > 8127 [i]