Best Known (205, 205+33, s)-Nets in Base 4
(205, 205+33, 16401)-Net over F4 — Constructive and digital
Digital (205, 238, 16401)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 21, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (184, 217, 16384)-net over F4, using
- net defined by OOA [i] based on linear OOA(4217, 16384, F4, 33, 33) (dual of [(16384, 33), 540455, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
- net defined by OOA [i] based on linear OOA(4217, 16384, F4, 33, 33) (dual of [(16384, 33), 540455, 34]-NRT-code), using
- digital (5, 21, 17)-net over F4, using
(205, 205+33, 165841)-Net over F4 — Digital
Digital (205, 238, 165841)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4238, 165841, F4, 33) (dual of [165841, 165603, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4238, 262169, F4, 33) (dual of [262169, 261931, 34]-code), using
- (u, u+v)-construction [i] based on
- linear OA(421, 24, F4, 16) (dual of [24, 3, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 25, F4, 16) (dual of [25, 4, 17]-code), using
- 3 times truncation [i] based on linear OA(424, 28, F4, 19) (dual of [28, 4, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 25, F4, 16) (dual of [25, 4, 17]-code), using
- linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(421, 24, F4, 16) (dual of [24, 3, 17]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4238, 262169, F4, 33) (dual of [262169, 261931, 34]-code), using
(205, 205+33, large)-Net in Base 4 — Upper bound on s
There is no (205, 238, large)-net in base 4, because
- 31 times m-reduction [i] would yield (205, 207, large)-net in base 4, but