MinT - Best Known (228−124, 228, s)-Nets in Base 4

Best Known (228−124, 228, s)-Nets in Base 4

(228−124, 228, 104)-Net over F₄ — Constructive and digital

Digital (104, 228, 104)-net over F₄, using

t-expansion [i] based on digital (73, 228, 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]

(228−124, 228, 144)-Net over F₄ — Digital

Digital (104, 228, 144)-net over F₄, using

t-expansion [i] based on digital (91, 228, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(228−124, 228, 1255)-Net in Base 4 — Upper bound on s

There is no (104, 228, 1256)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190847 355690 318737 300244 208068 254641 043797 222850 279406 194757 823815 702415 290892 510753 891756 568113 991159 044187 880284 616519 415344 297977 042200 > 4²²⁸ [i]