Best Known (34, 50, s)-Nets in Base 5
(34, 50, 208)-Net over F5 — Constructive and digital
Digital (34, 50, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 25, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
(34, 50, 414)-Net over F5 — Digital
Digital (34, 50, 414)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(550, 414, F5, 16) (dual of [414, 364, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(550, 630, F5, 16) (dual of [630, 580, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(549, 625, F5, 16) (dual of [625, 576, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(545, 625, F5, 14) (dual of [625, 580, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(550, 630, F5, 16) (dual of [630, 580, 17]-code), using
(34, 50, 21982)-Net in Base 5 — Upper bound on s
There is no (34, 50, 21983)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 88822 738055 349200 290955 063068 706785 > 550 [i]