Best Known (98, 98+69, s)-Nets in Base 8
(98, 98+69, 354)-Net over F8 — Constructive and digital
Digital (98, 167, 354)-net over F8, using
- t-expansion [i] based on digital (93, 167, 354)-net over F8, using
- 5 times m-reduction [i] based on digital (93, 172, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 86, 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, 86, 177)-net over F64, using
- 5 times m-reduction [i] based on digital (93, 172, 354)-net over F8, using
(98, 98+69, 602)-Net over F8 — Digital
Digital (98, 167, 602)-net over F8, using
(98, 98+69, 49590)-Net in Base 8 — Upper bound on s
There is no (98, 167, 49591)-net in base 8, because
- 1 times m-reduction [i] would yield (98, 166, 49591)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 818885 545758 591758 249108 909138 662541 357316 725506 969464 665503 748492 544320 324950 677383 313341 229526 073571 174045 146286 324655 738059 253881 013051 913789 696581 > 8166 [i]