MinT - Best Known (228−116, 228, s)-Nets in Base 4

Best Known (228−116, 228, s)-Nets in Base 4

(228−116, 228, 130)-Net over F₄ — Constructive and digital

Digital (112, 228, 130)-net over F₄, using

t-expansion [i] based on digital (105, 228, 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]

(228−116, 228, 165)-Net over F₄ — Digital

Digital (112, 228, 165)-net over F₄, using

t-expansion [i] based on digital (109, 228, 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]

(228−116, 228, 1693)-Net in Base 4 — Upper bound on s

There is no (112, 228, 1694)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 187535 787470 957591 982165 360466 921214 359220 249596 263554 376231 400601 277488 449094 702757 828432 642737 234972 583075 374828 454670 273903 835016 356728 > 4²²⁸ [i]