Best Known (186, 186+52, s)-Nets in Base 4
(186, 186+52, 1056)-Net over F4 — Constructive and digital
Digital (186, 238, 1056)-net over F4, using
- 42 times duplication [i] based on digital (184, 236, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 59, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
- trace code for nets [i] based on digital (7, 59, 264)-net over F256, using
(186, 186+52, 4301)-Net over F4 — Digital
Digital (186, 238, 4301)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4238, 4301, F4, 52) (dual of [4301, 4063, 53]-code), using
- 202 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0, 1, 65 times 0, 1, 95 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using
- 202 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0, 1, 65 times 0, 1, 95 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
(186, 186+52, 1141111)-Net in Base 4 — Upper bound on s
There is no (186, 238, 1141112)-net in base 4, because
- 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]