Best Known (122−39, 122, s)-Nets in Base 8
(122−39, 122, 402)-Net over F8 — Constructive and digital
Digital (83, 122, 402)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (11, 30, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- digital (53, 92, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 46, 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, 46, 177)-net over F64, using
- digital (11, 30, 48)-net over F8, using
(122−39, 122, 576)-Net in Base 8 — Constructive
(83, 122, 576)-net in base 8, using
- t-expansion [i] based on (81, 122, 576)-net in base 8, using
- 4 times m-reduction [i] based on (81, 126, 576)-net in base 8, using
- trace code for nets [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 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, 54, 288)-net over F128, using
- trace code for nets [i] based on (18, 63, 288)-net in base 64, using
- 4 times m-reduction [i] based on (81, 126, 576)-net in base 8, using
(122−39, 122, 1722)-Net over F8 — Digital
Digital (83, 122, 1722)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8122, 1722, F8, 39) (dual of [1722, 1600, 40]-code), using
- 1599 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 7 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 45 times 0, 1, 48 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0, 1, 60 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 79 times 0, 1, 84 times 0, 1, 89 times 0) [i] based on linear OA(839, 40, F8, 39) (dual of [40, 1, 40]-code or 40-arc in PG(38,8)), using
- dual of repetition code with length 40 [i]
- 1599 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 7 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 35 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 45 times 0, 1, 48 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0, 1, 60 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 79 times 0, 1, 84 times 0, 1, 89 times 0) [i] based on linear OA(839, 40, F8, 39) (dual of [40, 1, 40]-code or 40-arc in PG(38,8)), using
(122−39, 122, 638802)-Net in Base 8 — Upper bound on s
There is no (83, 122, 638803)-net in base 8, because
- 1 times m-reduction [i] would yield (83, 121, 638803)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 18 788471 366409 883081 554360 922239 319836 783852 869974 125339 022783 938619 407435 431689 870144 289952 785212 190672 973688 > 8121 [i]