Best Known (79, 79+45, s)-Nets in Base 9
(79, 79+45, 740)-Net over F9 — Constructive and digital
Digital (79, 124, 740)-net over F9, using
- 2 times m-reduction [i] based on digital (79, 126, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 63, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 63, 370)-net over F81, using
(79, 79+45, 1077)-Net over F9 — Digital
Digital (79, 124, 1077)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9124, 1077, F9, 45) (dual of [1077, 953, 46]-code), using
- 952 step Varšamov–Edel lengthening with (ri) = (7, 3, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 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, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 39 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0) [i] based on linear OA(945, 46, F9, 45) (dual of [46, 1, 46]-code or 46-arc in PG(44,9)), using
- dual of repetition code with length 46 [i]
- 952 step Varšamov–Edel lengthening with (ri) = (7, 3, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 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, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 39 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0) [i] based on linear OA(945, 46, F9, 45) (dual of [46, 1, 46]-code or 46-arc in PG(44,9)), using
(79, 79+45, 244806)-Net in Base 9 — Upper bound on s
There is no (79, 124, 244807)-net in base 9, because
- 1 times m-reduction [i] would yield (79, 123, 244807)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 2354 260569 246054 252902 665085 589185 116354 826083 794858 013117 832935 113567 703621 652694 502193 861835 666789 584597 328797 338065 > 9123 [i]