Best Known (155−49, 155, s)-Nets in Base 8
(155−49, 155, 1026)-Net over F8 — Constructive and digital
Digital (106, 155, 1026)-net over F8, using
- 1 times m-reduction [i] based on digital (106, 156, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 78, 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
- trace code for nets [i] based on digital (28, 78, 513)-net over F64, using
(155−49, 155, 2232)-Net over F8 — Digital
Digital (106, 155, 2232)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8155, 2232, F8, 49) (dual of [2232, 2077, 50]-code), using
- 2076 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 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, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 7 times 0, 1, 9 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 58 times 0, 1, 62 times 0, 1, 64 times 0, 1, 67 times 0, 1, 70 times 0, 1, 74 times 0, 1, 76 times 0, 1, 80 times 0, 1, 84 times 0, 1, 88 times 0, 1, 92 times 0) [i] based on linear OA(849, 50, F8, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,8)), using
- dual of repetition code with length 50 [i]
- 2076 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 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, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 7 times 0, 1, 9 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 41 times 0, 1, 43 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 58 times 0, 1, 62 times 0, 1, 64 times 0, 1, 67 times 0, 1, 70 times 0, 1, 74 times 0, 1, 76 times 0, 1, 80 times 0, 1, 84 times 0, 1, 88 times 0, 1, 92 times 0) [i] based on linear OA(849, 50, F8, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,8)), using
(155−49, 155, 873141)-Net in Base 8 — Upper bound on s
There is no (106, 155, 873142)-net in base 8, because
- 1 times m-reduction [i] would yield (106, 154, 873142)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 11 908651 817164 735041 686307 465907 716323 945267 555313 986815 737280 004598 845334 836797 748337 844460 071455 456037 487727 416582 271730 997547 490876 232756 > 8154 [i]