Best Known (236−52, 236, s)-Nets in Base 4
(236−52, 236, 1056)-Net over F4 — Constructive and digital
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
(236−52, 236, 4137)-Net over F4 — Digital
Digital (184, 236, 4137)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4236, 4137, F4, 52) (dual of [4137, 3901, 53]-code), using
- 40 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 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
- 40 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
(236−52, 236, 1025687)-Net in Base 4 — Upper bound on s
There is no (184, 236, 1025688)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12194 493046 824648 485965 952724 644186 052264 059413 481975 211168 466188 540227 200470 469566 291093 320234 789173 740527 784995 435748 734806 563218 603725 313200 > 4236 [i]