Best Known (100, 100+32, s)-Nets in Base 3
(100, 100+32, 400)-Net over F3 — Constructive and digital
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
(100, 100+32, 703)-Net over F3 — Digital
Digital (100, 132, 703)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3132, 703, F3, 32) (dual of [703, 571, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3132, 757, F3, 32) (dual of [757, 625, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
- linear OA(3124, 729, F3, 32) (dual of [729, 605, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3103, 729, F3, 26) (dual of [729, 626, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- construction X applied to Ce(31) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3132, 757, F3, 32) (dual of [757, 625, 33]-code), using
(100, 100+32, 29344)-Net in Base 3 — Upper bound on s
There is no (100, 132, 29345)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 955 156820 550502 026172 307023 807847 223377 337790 161051 763794 845505 > 3132 [i]