Best Known (101, 101+43, s)-Nets in Base 5
(101, 101+43, 400)-Net over F5 — Constructive and digital
Digital (101, 144, 400)-net over F5, using
- t-expansion [i] based on digital (100, 144, 400)-net over F5, using
- 6 times m-reduction [i] based on digital (100, 150, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 75, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- trace code for nets [i] based on digital (25, 75, 200)-net over F25, using
- 6 times m-reduction [i] based on digital (100, 150, 400)-net over F5, using
(101, 101+43, 1050)-Net over F5 — Digital
Digital (101, 144, 1050)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5144, 1050, F5, 43) (dual of [1050, 906, 44]-code), using
- 905 step Varšamov–Edel lengthening with (ri) = (10, 4, 3, 2, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 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, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 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, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 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, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 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, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0) [i] based on linear OA(543, 44, F5, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,5)), using
- dual of repetition code with length 44 [i]
- 905 step Varšamov–Edel lengthening with (ri) = (10, 4, 3, 2, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 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, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 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, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 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, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 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, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0) [i] based on linear OA(543, 44, F5, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,5)), using
(101, 101+43, 124747)-Net in Base 5 — Upper bound on s
There is no (101, 144, 124748)-net in base 5, because
- 1 times m-reduction [i] would yield (101, 143, 124748)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 8968 836824 883854 332880 736408 161821 038477 544629 221120 176576 903262 252651 370241 932691 198670 805831 222193 > 5143 [i]