Best Known (146−109, 146, s)-Nets in Base 8
(146−109, 146, 98)-Net over F8 — Constructive and digital
Digital (37, 146, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
(146−109, 146, 121)-Net over F8 — Digital
Digital (37, 146, 121)-net over F8, using
- net from sequence [i] based on digital (37, 120)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 121, using
(146−109, 146, 763)-Net in Base 8 — Upper bound on s
There is no (37, 146, 764)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 145, 764)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 94097 831741 414821 211659 562598 555603 172956 559235 534100 858307 012734 276934 838177 304810 922878 747470 273418 232477 827194 391861 388348 128062 > 8145 [i]