Best Known (101, 101+40, s)-Nets in Base 8
(101, 101+40, 1026)-Net over F8 — Constructive and digital
Digital (101, 141, 1026)-net over F8, using
- 5 times m-reduction [i] based on digital (101, 146, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 73, 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
- trace code for nets [i] based on digital (28, 73, 513)-net over F64, using
(101, 101+40, 4150)-Net over F8 — Digital
Digital (101, 141, 4150)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8141, 4150, F8, 40) (dual of [4150, 4009, 41]-code), using
- 54 step Varšamov–Edel lengthening with (ri) = (1, 53 times 0) [i] based on linear OA(8140, 4095, F8, 40) (dual of [4095, 3955, 41]-code), using
- 1 times truncation [i] based on linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using
- an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- 1 times truncation [i] based on linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using
- 54 step Varšamov–Edel lengthening with (ri) = (1, 53 times 0) [i] based on linear OA(8140, 4095, F8, 40) (dual of [4095, 3955, 41]-code), using
(101, 101+40, 2760518)-Net in Base 8 — Upper bound on s
There is no (101, 141, 2760519)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 21 661567 347355 921490 624841 364925 835338 567102 999434 831458 718289 322142 079268 503155 618299 871033 725034 268796 468278 006481 349148 809988 > 8141 [i]