Best Known (104, 135, s)-Nets in Base 5
(104, 135, 504)-Net over F5 — Constructive and digital
Digital (104, 135, 504)-net over F5, using
- 1 times m-reduction [i] based on digital (104, 136, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (36, 52, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 26, 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, 26, 126)-net over F25, using
- digital (52, 84, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 42, 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, 42, 126)-net over F25, using
- digital (36, 52, 252)-net over F5, using
- (u, u+v)-construction [i] based on
(104, 135, 4224)-Net over F5 — Digital
Digital (104, 135, 4224)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5135, 4224, F5, 31) (dual of [4224, 4089, 32]-code), using
- 1084 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 32 times 0, 1, 54 times 0, 1, 85 times 0, 1, 120 times 0, 1, 155 times 0, 1, 181 times 0, 1, 201 times 0, 1, 216 times 0) [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1084 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 32 times 0, 1, 54 times 0, 1, 85 times 0, 1, 120 times 0, 1, 155 times 0, 1, 181 times 0, 1, 201 times 0, 1, 216 times 0) [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
(104, 135, 2817325)-Net in Base 5 — Upper bound on s
There is no (104, 135, 2817326)-net in base 5, because
- 1 times m-reduction [i] would yield (104, 134, 2817326)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 4591 786257 080405 308642 054156 248213 310517 371493 424278 708957 273339 350448 457732 393067 664950 781145 > 5134 [i]