Best Known (93−22, 93, s)-Nets in Base 3
(93−22, 93, 400)-Net over F3 — Constructive and digital
Digital (71, 93, 400)-net over F3, using
- 31 times duplication [i] based on digital (70, 92, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 23, 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, 23, 100)-net over F81, using
(93−22, 93, 633)-Net over F3 — Digital
Digital (71, 93, 633)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(393, 633, F3, 22) (dual of [633, 540, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(393, 757, F3, 22) (dual of [757, 664, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(385, 729, F3, 22) (dual of [729, 644, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(361, 729, F3, 16) (dual of [729, 668, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(21) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(393, 757, F3, 22) (dual of [757, 664, 23]-code), using
(93−22, 93, 26525)-Net in Base 3 — Upper bound on s
There is no (71, 93, 26526)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 235 751235 627127 823998 622047 041912 360920 309297 > 393 [i]