Best Known (241−54, 241, s)-Nets in Base 4
(241−54, 241, 1052)-Net over F4 — Constructive and digital
Digital (187, 241, 1052)-net over F4, using
- 41 times duplication [i] based on digital (186, 240, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 60, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 60, 263)-net over F256, using
(241−54, 241, 4009)-Net over F4 — Digital
Digital (187, 241, 4009)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4241, 4009, F4, 54) (dual of [4009, 3768, 55]-code), using
- discarding factors / shortening the dual code based on linear OA(4241, 4096, F4, 54) (dual of [4096, 3855, 55]-code), using
- an extension Ce(53) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
- discarding factors / shortening the dual code based on linear OA(4241, 4096, F4, 54) (dual of [4096, 3855, 55]-code), using
(241−54, 241, 861424)-Net in Base 4 — Upper bound on s
There is no (187, 241, 861425)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12 487119 903710 026171 017460 751749 690159 350702 203394 983420 106737 878352 146973 241980 921879 785911 833031 862353 905018 699720 507849 426044 278997 740323 342752 > 4241 [i]