Best Known (150−36, 150, s)-Nets in Base 5
(150−36, 150, 504)-Net over F5 — Constructive and digital
Digital (114, 150, 504)-net over F5, using
- t-expansion [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
(150−36, 150, 3472)-Net over F5 — Digital
Digital (114, 150, 3472)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5150, 3472, F5, 36) (dual of [3472, 3322, 37]-code), using
- 338 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 30 times 0, 1, 57 times 0, 1, 94 times 0, 1, 128 times 0) [i] based on linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 338 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 14 times 0, 1, 30 times 0, 1, 57 times 0, 1, 94 times 0, 1, 128 times 0) [i] based on linear OA(5141, 3125, F5, 36) (dual of [3125, 2984, 37]-code), using
(150−36, 150, 1261291)-Net in Base 5 — Upper bound on s
There is no (114, 150, 1261292)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 700 649692 125897 147365 636596 588007 203059 079553 783649 371878 395625 032407 103382 535146 718109 894839 896132 335425 > 5150 [i]