Best Known (106−60, 106, s)-Nets in Base 7
(106−60, 106, 47)-Net over F7 — Constructive and digital
Digital (46, 106, 47)-net over F7, using
- net from sequence [i] based on digital (46, 46)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 46)-sequence over F49, using
- s-reduction based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- s-reduction based on digital (0, 49)-sequence over F49, using
- base reduction for sequences [i] based on digital (0, 46)-sequence over F49, using
(106−60, 106, 105)-Net over F7 — Digital
Digital (46, 106, 105)-net over F7, using
- t-expansion [i] based on digital (43, 106, 105)-net over F7, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
(106−60, 106, 1924)-Net in Base 7 — Upper bound on s
There is no (46, 106, 1925)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 384323 693057 632346 112782 754753 251522 104489 515374 936282 527426 950825 506125 294824 671055 131353 > 7106 [i]