Best Known (52−16, 52, s)-Nets in Base 4
(52−16, 52, 240)-Net over F4 — Constructive and digital
Digital (36, 52, 240)-net over F4, using
- 41 times duplication [i] based on digital (35, 51, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 17, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 17, 80)-net over F64, using
(52−16, 52, 281)-Net over F4 — Digital
Digital (36, 52, 281)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(452, 281, F4, 16) (dual of [281, 229, 17]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 11 times 0) [i] based on linear OA(448, 256, F4, 16) (dual of [256, 208, 17]-code), using
- 1 times truncation [i] based on linear OA(449, 257, F4, 17) (dual of [257, 208, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 257 | 48−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(449, 257, F4, 17) (dual of [257, 208, 18]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 11 times 0) [i] based on linear OA(448, 256, F4, 16) (dual of [256, 208, 17]-code), using
(52−16, 52, 10273)-Net in Base 4 — Upper bound on s
There is no (36, 52, 10274)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 20 297860 553706 658742 813763 095932 > 452 [i]