Best Known (104, 104+41, s)-Nets in Base 8
(104, 104+41, 1026)-Net over F8 — Constructive and digital
Digital (104, 145, 1026)-net over F8, using
- 7 times m-reduction [i] based on digital (104, 152, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 76, 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, 76, 513)-net over F64, using
(104, 104+41, 4281)-Net over F8 — Digital
Digital (104, 145, 4281)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8145, 4281, F8, 41) (dual of [4281, 4136, 42]-code), using
- 181 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 43 times 0, 1, 129 times 0) [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]
- 181 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 43 times 0, 1, 129 times 0) [i] based on linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using
(104, 104+41, 3770983)-Net in Base 8 — Upper bound on s
There is no (104, 145, 3770984)-net in base 8, because
- 1 times m-reduction [i] would yield (104, 144, 3770984)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 11090 686792 968889 262220 610871 560373 293025 686578 646021 468746 654210 779483 218983 107260 310075 788038 790504 857495 256182 703565 249109 426782 > 8144 [i]