Best Known (75, 170, s)-Nets in Base 8
(75, 170, 130)-Net over F8 — Constructive and digital
Digital (75, 170, 130)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 61, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (14, 109, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8 (see above)
- digital (14, 61, 65)-net over F8, using
(75, 170, 174)-Net over F8 — Digital
Digital (75, 170, 174)-net over F8, using
(75, 170, 4607)-Net in Base 8 — Upper bound on s
There is no (75, 170, 4608)-net in base 8, because
- 1 times m-reduction [i] would yield (75, 169, 4608)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 419 733594 927840 297128 305222 277309 758560 643751 302916 903965 813140 966604 468841 122385 048178 999565 763540 855552 593224 388997 214436 683390 550310 547936 996212 700689 > 8169 [i]