Best Known (252−121, 252, s)-Nets in Base 4
(252−121, 252, 130)-Net over F4 — Constructive and digital
Digital (131, 252, 130)-net over F4, using
- t-expansion [i] based on digital (105, 252, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(252−121, 252, 200)-Net over F4 — Digital
Digital (131, 252, 200)-net over F4, using
(252−121, 252, 2502)-Net in Base 4 — Upper bound on s
There is no (131, 252, 2503)-net in base 4, because
- 1 times m-reduction [i] would yield (131, 251, 2503)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13 223233 436622 788494 268129 971017 433887 503718 883061 489317 128541 141893 699565 728687 761485 580076 943247 731876 071324 122694 931856 332522 099083 344752 858908 085096 > 4251 [i]