Best Known (33−16, 33, s)-Nets in Base 25
(33−16, 33, 132)-Net over F25 — Constructive and digital
Digital (17, 33, 132)-net over F25, using
- 2 times m-reduction [i] based on digital (17, 35, 132)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (4, 22, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25 (see above)
- digital (4, 13, 66)-net over F25, using
- (u, u+v)-construction [i] based on
(33−16, 33, 389)-Net over F25 — Digital
Digital (17, 33, 389)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2533, 389, F25, 16) (dual of [389, 356, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2533, 633, F25, 16) (dual of [633, 600, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(2531, 625, F25, 16) (dual of [625, 594, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2525, 625, F25, 13) (dual of [625, 600, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(2533, 633, F25, 16) (dual of [633, 600, 17]-code), using
(33−16, 33, 91614)-Net in Base 25 — Upper bound on s
There is no (17, 33, 91615)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 13553 375361 587340 119159 938804 290223 237821 978433 > 2533 [i]