Best Known (103, 103+46, s)-Nets in Base 8
(103, 103+46, 1026)-Net over F8 — Constructive and digital
Digital (103, 149, 1026)-net over F8, using
- 1 times m-reduction [i] based on digital (103, 150, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 75, 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, 75, 513)-net over F64, using
(103, 103+46, 2485)-Net over F8 — Digital
Digital (103, 149, 2485)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8149, 2485, F8, 46) (dual of [2485, 2336, 47]-code), using
- 2335 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 1, 1, 1, 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, 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, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 17 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, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 59 times 0, 1, 62 times 0, 1, 65 times 0, 1, 68 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0, 1, 82 times 0, 1, 87 times 0, 1, 90 times 0, 1, 95 times 0, 1, 99 times 0, 1, 104 times 0, 1, 110 times 0) [i] based on linear OA(846, 47, F8, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,8)), using
- dual of repetition code with length 47 [i]
- 2335 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 1, 1, 1, 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, 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, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 17 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, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 59 times 0, 1, 62 times 0, 1, 65 times 0, 1, 68 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0, 1, 82 times 0, 1, 87 times 0, 1, 90 times 0, 1, 95 times 0, 1, 99 times 0, 1, 104 times 0, 1, 110 times 0) [i] based on linear OA(846, 47, F8, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,8)), using
(103, 103+46, 954562)-Net in Base 8 — Upper bound on s
There is no (103, 149, 954563)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 363 425754 385022 426783 321939 499703 656920 735599 742691 348146 919109 648075 153783 974295 988994 682722 301364 198766 860764 235874 401822 458633 861824 > 8149 [i]