Best Known (186, 186+53, s)-Nets in Base 4
(186, 186+53, 1052)-Net over F4 — Constructive and digital
Digital (186, 239, 1052)-net over F4, using
- 1 times m-reduction [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
(186, 186+53, 4132)-Net over F4 — Digital
Digital (186, 239, 4132)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4239, 4132, F4, 53) (dual of [4132, 3893, 54]-code), using
- 32 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0) [i] based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
- an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- 32 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0) [i] based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
(186, 186+53, 1141111)-Net in Base 4 — Upper bound on s
There is no (186, 239, 1141112)-net in base 4, because
- 1 times m-reduction [i] would yield (186, 238, 1141112)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 195109 370235 051273 386565 403139 704652 296273 865306 702867 569592 517289 586610 713442 179881 713504 857508 601941 708858 034814 148813 283141 884711 808159 816252 > 4238 [i]