Best Known (121−46, 121, s)-Nets in Base 8
(121−46, 121, 354)-Net over F8 — Constructive and digital
Digital (75, 121, 354)-net over F8, using
- 15 times m-reduction [i] based on digital (75, 136, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 68, 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, 68, 177)-net over F64, using
(121−46, 121, 432)-Net in Base 8 — Constructive
(75, 121, 432)-net in base 8, using
- 1 times m-reduction [i] based on (75, 122, 432)-net in base 8, using
- trace code for nets [i] based on (14, 61, 216)-net in base 64, using
- 2 times m-reduction [i] based on (14, 63, 216)-net in base 64, using
- base change [i] based on digital (5, 54, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 54, 216)-net over F128, using
- 2 times m-reduction [i] based on (14, 63, 216)-net in base 64, using
- trace code for nets [i] based on (14, 61, 216)-net in base 64, using
(121−46, 121, 692)-Net over F8 — Digital
Digital (75, 121, 692)-net over F8, using
(121−46, 121, 75912)-Net in Base 8 — Upper bound on s
There is no (75, 121, 75913)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 18 789339 005753 926108 973544 136031 654725 883977 456823 751476 799534 767367 500030 052190 470744 598391 148806 183983 267904 > 8121 [i]