Best Known (71, 71+44, s)-Nets in Base 8
(71, 71+44, 354)-Net over F8 — Constructive and digital
Digital (71, 115, 354)-net over F8, using
- 13 times m-reduction [i] based on digital (71, 128, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 64, 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, 64, 177)-net over F64, using
(71, 71+44, 384)-Net in Base 8 — Constructive
(71, 115, 384)-net in base 8, using
- 3 times m-reduction [i] based on (71, 118, 384)-net in base 8, using
- trace code for nets [i] based on (12, 59, 192)-net in base 64, using
- 4 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
- base change [i] based on digital (3, 54, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 54, 192)-net over F128, using
- 4 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
- trace code for nets [i] based on (12, 59, 192)-net in base 64, using
(71, 71+44, 644)-Net over F8 — Digital
Digital (71, 115, 644)-net over F8, using
(71, 71+44, 67977)-Net in Base 8 — Upper bound on s
There is no (71, 115, 67978)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 71 682301 101075 829665 378118 251805 476090 273764 143937 566377 755598 039733 293989 338156 506003 740150 709787 383712 > 8115 [i]