Best Known (116, 116+27, s)-Nets in Base 3
(116, 116+27, 688)-Net over F3 — Constructive and digital
Digital (116, 143, 688)-net over F3, using
- t-expansion [i] based on digital (115, 143, 688)-net over F3, using
- 1 times m-reduction [i] based on digital (115, 144, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 36, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 36, 172)-net over F81, using
- 1 times m-reduction [i] based on digital (115, 144, 688)-net over F3, using
(116, 116+27, 2587)-Net over F3 — Digital
Digital (116, 143, 2587)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3143, 2587, F3, 27) (dual of [2587, 2444, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3143, 3280, F3, 27) (dual of [3280, 3137, 28]-code), using
(116, 116+27, 461313)-Net in Base 3 — Upper bound on s
There is no (116, 143, 461314)-net in base 3, because
- 1 times m-reduction [i] would yield (116, 142, 461314)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 56 392176 689840 311959 119380 976423 384380 020002 229563 047799 975453 060685 > 3142 [i]