Best Known (140−42, 140, s)-Nets in Base 5
(140−42, 140, 400)-Net over F5 — Constructive and digital
Digital (98, 140, 400)-net over F5, using
- 6 times m-reduction [i] based on digital (98, 146, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 73, 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, 73, 200)-net over F25, using
(140−42, 140, 1004)-Net over F5 — Digital
Digital (98, 140, 1004)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5140, 1004, F5, 42) (dual of [1004, 864, 43]-code), using
- 863 step Varšamov–Edel lengthening with (ri) = (10, 4, 3, 2, 1, 1, 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, 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, 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, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 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, 9 times 0, 1, 9 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, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0) [i] based on linear OA(542, 43, F5, 42) (dual of [43, 1, 43]-code or 43-arc in PG(41,5)), using
- dual of repetition code with length 43 [i]
- 863 step Varšamov–Edel lengthening with (ri) = (10, 4, 3, 2, 1, 1, 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, 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, 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, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 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, 9 times 0, 1, 9 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, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 36 times 0) [i] based on linear OA(542, 43, F5, 42) (dual of [43, 1, 43]-code or 43-arc in PG(41,5)), using
(140−42, 140, 99121)-Net in Base 5 — Upper bound on s
There is no (98, 140, 99122)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 71 761259 103754 979682 286635 139284 678634 129277 485933 472296 012090 746139 745058 590900 516614 928352 331209 > 5140 [i]