Best Known (110, 147, s)-Nets in Base 5
(110, 147, 420)-Net over F5 — Constructive and digital
Digital (110, 147, 420)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (5, 23, 20)-net over F5, using
- net from sequence [i] based on digital (5, 19)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 5 and N(F) ≥ 20, using
- net from sequence [i] based on digital (5, 19)-sequence over F5, using
- digital (87, 124, 400)-net over F5, using
- trace code for nets [i] based on digital (25, 62, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- trace code for nets [i] based on digital (25, 62, 200)-net over F25, using
- digital (5, 23, 20)-net over F5, using
(110, 147, 2839)-Net over F5 — Digital
Digital (110, 147, 2839)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5147, 2839, F5, 37) (dual of [2839, 2692, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(5147, 3131, F5, 37) (dual of [3131, 2984, 38]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5146, 3130, F5, 37) (dual of [3130, 2984, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- linear OA(5146, 3125, F5, 37) (dual of [3125, 2979, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 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]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5146, 3130, F5, 37) (dual of [3130, 2984, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(5147, 3131, F5, 37) (dual of [3131, 2984, 38]-code), using
(110, 147, 882037)-Net in Base 5 — Upper bound on s
There is no (110, 147, 882038)-net in base 5, because
- 1 times m-reduction [i] would yield (110, 146, 882038)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1 121050 981169 403558 243552 617138 881399 051829 020578 004152 348176 432995 920609 649578 814636 140737 799928 650625 > 5146 [i]