Best Known (111, 167, s)-Nets in Base 8
(111, 167, 513)-Net over F8 — Constructive and digital
Digital (111, 167, 513)-net over F8, using
- base reduction for projective spaces (embedding PG(83,64) in PG(166,8)) for nets [i] based on digital (28, 84, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(111, 167, 576)-Net in Base 8 — Constructive
(111, 167, 576)-net in base 8, using
- t-expansion [i] based on (108, 167, 576)-net in base 8, using
- 5 times m-reduction [i] based on (108, 172, 576)-net in base 8, using
- trace code for nets [i] based on (22, 86, 288)-net in base 64, using
- 5 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 5 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- trace code for nets [i] based on (22, 86, 288)-net in base 64, using
- 5 times m-reduction [i] based on (108, 172, 576)-net in base 8, using
(111, 167, 1711)-Net over F8 — Digital
Digital (111, 167, 1711)-net over F8, using
(111, 167, 392802)-Net in Base 8 — Upper bound on s
There is no (111, 167, 392803)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 6 546969 615203 156267 349017 068652 703765 299008 808875 533008 092788 025897 411148 610638 512506 616651 786208 368542 751985 495686 027005 587305 259574 158910 649423 688952 > 8167 [i]