Best Known (33, 67, s)-Nets in Base 32
(33, 67, 202)-Net over F32 — Constructive and digital
Digital (33, 67, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 24, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (9, 43, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (7, 24, 98)-net over F32, using
(33, 67, 288)-Net in Base 32 — Constructive
(33, 67, 288)-net in base 32, using
- 17 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
- base change [i] based on digital (9, 60, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 60, 288)-net over F128, using
(33, 67, 516)-Net over F32 — Digital
Digital (33, 67, 516)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3267, 516, F32, 2, 34) (dual of [(516, 2), 965, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3267, 1032, F32, 34) (dual of [1032, 965, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- linear OA(3264, 1024, F32, 34) (dual of [1024, 960, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3259, 1024, F32, 30) (dual of [1024, 965, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(323, 8, F32, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,32) or 8-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- OOA 2-folding [i] based on linear OA(3267, 1032, F32, 34) (dual of [1032, 965, 35]-code), using
(33, 67, 197982)-Net in Base 32 — Upper bound on s
There is no (33, 67, 197983)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 69996 022430 683835 270226 094168 398638 571159 420502 700797 742703 332833 272353 659398 667124 527233 113585 650750 > 3267 [i]