Best Known (41, 41+28, s)-Nets in Base 25
(41, 41+28, 288)-Net over F25 — Constructive and digital
Digital (41, 69, 288)-net over F25, using
- net from sequence [i] based on digital (41, 287)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 41 and N(F) ≥ 288, using
(41, 41+28, 1715)-Net over F25 — Digital
Digital (41, 69, 1715)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2569, 1715, F25, 28) (dual of [1715, 1646, 29]-code), using
- 1645 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 9 times 0, 1, 10 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 26 times 0, 1, 30 times 0, 1, 34 times 0, 1, 39 times 0, 1, 43 times 0, 1, 50 times 0, 1, 56 times 0, 1, 63 times 0, 1, 72 times 0, 1, 81 times 0, 1, 91 times 0, 1, 104 times 0, 1, 116 times 0, 1, 132 times 0, 1, 149 times 0, 1, 167 times 0, 1, 190 times 0) [i] based on linear OA(2528, 29, F25, 28) (dual of [29, 1, 29]-code or 29-arc in PG(27,25)), using
- dual of repetition code with length 29 [i]
- 1645 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 9 times 0, 1, 10 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 26 times 0, 1, 30 times 0, 1, 34 times 0, 1, 39 times 0, 1, 43 times 0, 1, 50 times 0, 1, 56 times 0, 1, 63 times 0, 1, 72 times 0, 1, 81 times 0, 1, 91 times 0, 1, 104 times 0, 1, 116 times 0, 1, 132 times 0, 1, 149 times 0, 1, 167 times 0, 1, 190 times 0) [i] based on linear OA(2528, 29, F25, 28) (dual of [29, 1, 29]-code or 29-arc in PG(27,25)), using
(41, 41+28, 1954753)-Net in Base 25 — Upper bound on s
There is no (41, 69, 1954754)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2 869859 338340 612974 719833 773672 519879 899932 441919 729253 320768 648349 432172 155555 191962 092060 134625 > 2569 [i]