MinT - Best Known (109, 109+138, s)-Nets in Base 4

Best Known (109, 109+138, s)-Nets in Base 4

(109, 109+138, 130)-Net over F₄ — Constructive and digital

Digital (109, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(109, 109+138, 165)-Net over F₄ — Digital

Digital (109, 247, 165)-net over F₄, using

net from sequence [i] based on digital (109, 164)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
  - Drinfeld modules of rank 1 [i]

(109, 109+138, 1207)-Net in Base 4 — Upper bound on s

There is no (109, 247, 1208)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51237 946194 245412 520881 557457 760069 422147 833141 929207 207147 836264 359468 377508 530727 718552 344222 120227 669179 198466 884856 775502 999459 454161 778148 998630 > 4²⁴⁷ [i]