Best Known (114, 114+33, s)-Nets in Base 5
(114, 114+33, 504)-Net over F5 — Constructive and digital
Digital (114, 147, 504)-net over F5, using
- t-expansion [i] based on digital (113, 147, 504)-net over F5, using
- 3 times m-reduction [i] based on digital (113, 150, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (38, 56, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 28, 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
- trace code for nets [i] based on digital (10, 28, 126)-net over F25, using
- digital (57, 94, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 47, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- trace code for nets [i] based on digital (10, 47, 126)-net over F25, using
- digital (38, 56, 252)-net over F5, using
- (u, u+v)-construction [i] based on
- 3 times m-reduction [i] based on digital (113, 150, 504)-net over F5, using
(114, 114+33, 5213)-Net over F5 — Digital
Digital (114, 147, 5213)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5147, 5213, F5, 33) (dual of [5213, 5066, 34]-code), using
- 5065 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 1, 1, 1, 1, 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, 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, 4 times 0, 1, 4 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, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 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, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 52 times 0, 1, 54 times 0, 1, 57 times 0, 1, 61 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 74 times 0, 1, 78 times 0, 1, 82 times 0, 1, 87 times 0, 1, 91 times 0, 1, 96 times 0, 1, 101 times 0, 1, 107 times 0, 1, 112 times 0, 1, 118 times 0, 1, 124 times 0, 1, 130 times 0, 1, 138 times 0, 1, 144 times 0, 1, 152 times 0, 1, 160 times 0, 1, 169 times 0, 1, 177 times 0, 1, 187 times 0, 1, 196 times 0, 1, 206 times 0, 1, 218 times 0, 1, 228 times 0, 1, 241 times 0, 1, 253 times 0) [i] based on linear OA(533, 34, F5, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,5)), using
- dual of repetition code with length 34 [i]
- 5065 step Varšamov–Edel lengthening with (ri) = (8, 3, 2, 2, 1, 1, 1, 1, 1, 1, 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, 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, 4 times 0, 1, 4 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, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 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, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 52 times 0, 1, 54 times 0, 1, 57 times 0, 1, 61 times 0, 1, 63 times 0, 1, 67 times 0, 1, 71 times 0, 1, 74 times 0, 1, 78 times 0, 1, 82 times 0, 1, 87 times 0, 1, 91 times 0, 1, 96 times 0, 1, 101 times 0, 1, 107 times 0, 1, 112 times 0, 1, 118 times 0, 1, 124 times 0, 1, 130 times 0, 1, 138 times 0, 1, 144 times 0, 1, 152 times 0, 1, 160 times 0, 1, 169 times 0, 1, 177 times 0, 1, 187 times 0, 1, 196 times 0, 1, 206 times 0, 1, 218 times 0, 1, 228 times 0, 1, 241 times 0, 1, 253 times 0) [i] based on linear OA(533, 34, F5, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,5)), using
(114, 114+33, 4060493)-Net in Base 5 — Upper bound on s
There is no (114, 147, 4060494)-net in base 5, because
- 1 times m-reduction [i] would yield (114, 146, 4060494)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1 121042 085119 760221 312774 861822 756259 056598 302937 623892 620811 095669 607352 318670 767994 768017 871628 084993 > 5146 [i]