Best Known (64, 64+39, s)-Nets in Base 25
(64, 64+39, 378)-Net over F25 — Constructive and digital
Digital (64, 103, 378)-net over F25, using
- t-expansion [i] based on digital (63, 103, 378)-net over F25, using
- 1 times m-reduction [i] based on digital (63, 104, 378)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (10, 23, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (10, 30, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- digital (10, 51, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- digital (10, 23, 126)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- 1 times m-reduction [i] based on digital (63, 104, 378)-net over F25, using
(64, 64+39, 3872)-Net over F25 — Digital
Digital (64, 103, 3872)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25103, 3872, F25, 39) (dual of [3872, 3769, 40]-code), using
- 3768 step Varšamov–Edel lengthening with (ri) = (3, 2, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 24 times 0, 1, 28 times 0, 1, 29 times 0, 1, 33 times 0, 1, 36 times 0, 1, 39 times 0, 1, 42 times 0, 1, 47 times 0, 1, 51 times 0, 1, 55 times 0, 1, 61 times 0, 1, 66 times 0, 1, 72 times 0, 1, 78 times 0, 1, 86 times 0, 1, 94 times 0, 1, 102 times 0, 1, 111 times 0, 1, 121 times 0, 1, 132 times 0, 1, 144 times 0, 1, 157 times 0, 1, 171 times 0, 1, 186 times 0, 1, 203 times 0, 1, 221 times 0, 1, 241 times 0, 1, 262 times 0, 1, 286 times 0, 1, 311 times 0) [i] based on linear OA(2539, 40, F25, 39) (dual of [40, 1, 40]-code or 40-arc in PG(38,25)), using
- dual of repetition code with length 40 [i]
- 3768 step Varšamov–Edel lengthening with (ri) = (3, 2, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 24 times 0, 1, 28 times 0, 1, 29 times 0, 1, 33 times 0, 1, 36 times 0, 1, 39 times 0, 1, 42 times 0, 1, 47 times 0, 1, 51 times 0, 1, 55 times 0, 1, 61 times 0, 1, 66 times 0, 1, 72 times 0, 1, 78 times 0, 1, 86 times 0, 1, 94 times 0, 1, 102 times 0, 1, 111 times 0, 1, 121 times 0, 1, 132 times 0, 1, 144 times 0, 1, 157 times 0, 1, 171 times 0, 1, 186 times 0, 1, 203 times 0, 1, 221 times 0, 1, 241 times 0, 1, 262 times 0, 1, 286 times 0, 1, 311 times 0) [i] based on linear OA(2539, 40, F25, 39) (dual of [40, 1, 40]-code or 40-arc in PG(38,25)), using
(64, 64+39, large)-Net in Base 25 — Upper bound on s
There is no (64, 103, large)-net in base 25, because
- 37 times m-reduction [i] would yield (64, 66, large)-net in base 25, but