Best Known (62, 62+43, s)-Nets in Base 8
(62, 62+43, 354)-Net over F8 — Constructive and digital
Digital (62, 105, 354)-net over F8, using
- 5 times m-reduction [i] based on digital (62, 110, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 55, 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, 55, 177)-net over F64, using
(62, 62+43, 429)-Net over F8 — Digital
Digital (62, 105, 429)-net over F8, using
(62, 62+43, 36786)-Net in Base 8 — Upper bound on s
There is no (62, 105, 36787)-net in base 8, because
- 1 times m-reduction [i] would yield (62, 104, 36787)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 8346 776151 728595 253602 337999 577760 348457 432738 100356 909009 504536 037769 411211 435771 171014 837040 > 8104 [i]