Best Known (100, 139, s)-Nets in Base 5
(100, 139, 408)-Net over F5 — Constructive and digital
Digital (100, 139, 408)-net over F5, using
- 1 times m-reduction [i] based on digital (100, 140, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 70, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- trace code for nets [i] based on digital (30, 70, 204)-net over F25, using
(100, 139, 1373)-Net over F5 — Digital
Digital (100, 139, 1373)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5139, 1373, F5, 39) (dual of [1373, 1234, 40]-code), using
- 1233 step Varšamov–Edel lengthening with (ri) = (9, 4, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 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, 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, 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, 8 times 0, 1, 8 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, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 42 times 0, 1, 43 times 0, 1, 46 times 0, 1, 47 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0) [i] based on linear OA(539, 40, F5, 39) (dual of [40, 1, 40]-code or 40-arc in PG(38,5)), using
- dual of repetition code with length 40 [i]
- 1233 step Varšamov–Edel lengthening with (ri) = (9, 4, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 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, 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, 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, 8 times 0, 1, 8 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, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 42 times 0, 1, 43 times 0, 1, 46 times 0, 1, 47 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0) [i] based on linear OA(539, 40, F5, 39) (dual of [40, 1, 40]-code or 40-arc in PG(38,5)), using
(100, 139, 236515)-Net in Base 5 — Upper bound on s
There is no (100, 139, 236516)-net in base 5, because
- 1 times m-reduction [i] would yield (100, 138, 236516)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 2 869953 673168 380375 442177 643133 912052 238721 341529 054867 129986 454514 909280 397807 520100 855264 276625 > 5138 [i]