Best Known (240−52, 240, s)-Nets in Base 4
(240−52, 240, 1539)-Net over F4 — Constructive and digital
Digital (188, 240, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 80, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(240−52, 240, 4534)-Net over F4 — Digital
Digital (188, 240, 4534)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4240, 4534, F4, 52) (dual of [4534, 4294, 53]-code), using
- 433 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0, 1, 65 times 0, 1, 95 times 0, 1, 111 times 0, 1, 118 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
- 433 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 29 times 0, 1, 65 times 0, 1, 95 times 0, 1, 111 times 0, 1, 118 times 0) [i] based on linear OA(4234, 4095, F4, 52) (dual of [4095, 3861, 53]-code), using
(240−52, 240, 1269525)-Net in Base 4 — Upper bound on s
There is no (188, 240, 1269526)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 121788 306901 374488 944048 444527 233201 220972 899342 667909 015374 096879 689555 705276 925726 388552 319053 384144 354036 211331 848943 513522 397925 018491 828928 > 4240 [i]