Best Known (68, 68+42, s)-Nets in Base 8
(68, 68+42, 354)-Net over F8 — Constructive and digital
Digital (68, 110, 354)-net over F8, using
- 12 times m-reduction [i] based on digital (68, 122, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 61, 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, 61, 177)-net over F64, using
(68, 68+42, 432)-Net in Base 8 — Constructive
(68, 110, 432)-net in base 8, using
- trace code for nets [i] based on (13, 55, 216)-net in base 64, using
- 1 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
- base change [i] based on digital (5, 48, 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, 48, 216)-net over F128, using
- 1 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
(68, 68+42, 629)-Net over F8 — Digital
Digital (68, 110, 629)-net over F8, using
(68, 68+42, 66647)-Net in Base 8 — Upper bound on s
There is no (68, 110, 66648)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2187 878154 336802 995794 236850 914434 265193 756421 336059 681575 692652 755942 189661 682784 937242 276346 906327 > 8110 [i]