MinT - Best Known (244−162, 244, s)-Nets in Base 4

Best Known (244−162, 244, s)-Nets in Base 4

(244−162, 244, 104)-Net over F₄ — Constructive and digital

Digital (82, 244, 104)-net over F₄, using

t-expansion [i] based on digital (73, 244, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(244−162, 244, 129)-Net over F₄ — Digital

Digital (82, 244, 129)-net over F₄, using

t-expansion [i] based on digital (81, 244, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(244−162, 244, 607)-Net in Base 4 — Upper bound on s

There is no (82, 244, 608)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 852 858040 792260 964386 795357 994545 567962 774537 256628 346483 572689 286050 510978 097649 183818 545326 874346 310227 611407 155267 312831 176340 006864 913390 595955 > 4²⁴⁴ [i]