Best Known (100, 131, s)-Nets in Base 3
(100, 131, 400)-Net over F3 — Constructive and digital
Digital (100, 131, 400)-net over F3, using
- 1 times m-reduction [i] based on digital (100, 132, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 33, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 33, 100)-net over F81, using
(100, 131, 778)-Net over F3 — Digital
Digital (100, 131, 778)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3131, 778, F3, 31) (dual of [778, 647, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3131, 786, F3, 31) (dual of [786, 655, 32]-code), using
- 44 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 8 times 0, 1, 10 times 0) [i] based on linear OA(3118, 729, F3, 31) (dual of [729, 611, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 44 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 8 times 0, 1, 10 times 0) [i] based on linear OA(3118, 729, F3, 31) (dual of [729, 611, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3131, 786, F3, 31) (dual of [786, 655, 32]-code), using
(100, 131, 43817)-Net in Base 3 — Upper bound on s
There is no (100, 131, 43818)-net in base 3, because
- 1 times m-reduction [i] would yield (100, 130, 43818)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 106 143559 476453 382924 683020 123993 620722 407890 132703 613083 377785 > 3130 [i]