Best Known (100, 100+41, s)-Nets in Base 8
(100, 100+41, 1026)-Net over F8 — Constructive and digital
Digital (100, 141, 1026)-net over F8, using
- 3 times m-reduction [i] based on digital (100, 144, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 72, 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, 72, 513)-net over F64, using
(100, 100+41, 3815)-Net over F8 — Digital
Digital (100, 141, 3815)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8141, 3815, F8, 41) (dual of [3815, 3674, 42]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using
(100, 100+41, 2487917)-Net in Base 8 — Upper bound on s
There is no (100, 141, 2487918)-net in base 8, because
- 1 times m-reduction [i] would yield (100, 140, 2487918)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 2 707700 151222 124073 211586 554519 980541 662909 231815 422608 800738 760005 631811 807285 173605 752787 993983 974629 123451 422063 791217 916698 > 8140 [i]