Best Known (94, 94+36, s)-Nets in Base 8
(94, 94+36, 1026)-Net over F8 — Constructive and digital
Digital (94, 130, 1026)-net over F8, using
- 2 times m-reduction [i] based on digital (94, 132, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 66, 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, 66, 513)-net over F64, using
(94, 94+36, 4519)-Net over F8 — Digital
Digital (94, 130, 4519)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8130, 4519, F8, 36) (dual of [4519, 4389, 37]-code), using
- 414 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 43 times 0, 1, 138 times 0, 1, 223 times 0) [i] based on linear OA(8125, 4100, F8, 36) (dual of [4100, 3975, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- linear OA(8125, 4096, F8, 36) (dual of [4096, 3971, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8121, 4096, F8, 35) (dual of [4096, 3975, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(80, 4, F8, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- 414 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 43 times 0, 1, 138 times 0, 1, 223 times 0) [i] based on linear OA(8125, 4100, F8, 36) (dual of [4100, 3975, 37]-code), using
(94, 94+36, 3592090)-Net in Base 8 — Upper bound on s
There is no (94, 130, 3592091)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2521 736704 000728 056078 490839 130762 878487 051189 489301 320344 350245 041361 917513 010288 289190 304245 994220 910354 982402 481835 > 8130 [i]