MinT - Best Known (228−118, 228, s)-Nets in Base 4

Best Known (228−118, 228, s)-Nets in Base 4

(228−118, 228, 130)-Net over F₄ — Constructive and digital

Digital (110, 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]

(228−118, 228, 165)-Net over F₄ — Digital

Digital (110, 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]

(228−118, 228, 1565)-Net in Base 4 — Upper bound on s

There is no (110, 228, 1566)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 188911 987691 496233 852494 454161 852019 147635 007222 863802 059886 529727 477135 994896 867619 690386 226359 929981 595812 202165 633186 764196 533653 352544 > 4²²⁸ [i]