Best Known (67, 67+44, s)-Nets in Base 8
(67, 67+44, 354)-Net over F8 — Constructive and digital
Digital (67, 111, 354)-net over F8, using
- 9 times m-reduction [i] based on digital (67, 120, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 60, 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, 60, 177)-net over F64, using
(67, 67+44, 384)-Net in Base 8 — Constructive
(67, 111, 384)-net in base 8, using
- 1 times m-reduction [i] based on (67, 112, 384)-net in base 8, using
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 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, 48, 192)-net over F128, using
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
(67, 67+44, 525)-Net over F8 — Digital
Digital (67, 111, 525)-net over F8, using
(67, 67+44, 46572)-Net in Base 8 — Upper bound on s
There is no (67, 111, 46573)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 17504 155782 906569 670312 668130 884739 989309 210636 331560 456942 325586 918827 820917 903255 796267 986739 298552 > 8111 [i]