Best Known (122, 122+118, s)-Nets in Base 3
(122, 122+118, 78)-Net over F3 — Constructive and digital
Digital (122, 240, 78)-net over F3, using
- t-expansion [i] based on digital (121, 240, 78)-net over F3, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
(122, 122+118, 123)-Net over F3 — Digital
Digital (122, 240, 123)-net over F3, using
(122, 122+118, 938)-Net in Base 3 — Upper bound on s
There is no (122, 240, 939)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3 303271 970470 795353 156526 432076 530813 449659 053290 070033 390662 287547 241515 617032 281912 195249 053959 448721 700710 841947 > 3240 [i]