MinT - Best Known (227−130, 227, s)-Nets in Base 4

Best Known (227−130, 227, s)-Nets in Base 4

(227−130, 227, 104)-Net over F₄ — Constructive and digital

Digital (97, 227, 104)-net over F₄, using

t-expansion [i] based on digital (73, 227, 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]

(227−130, 227, 144)-Net over F₄ — Digital

Digital (97, 227, 144)-net over F₄, using

t-expansion [i] based on digital (91, 227, 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]

(227−130, 227, 1004)-Net in Base 4 — Upper bound on s

There is no (97, 227, 1005)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47739 814482 275753 266243 330398 585752 078969 580340 446472 395068 961439 934183 410472 687036 515570 875330 651310 733475 671319 626506 538804 228178 147304 > 4²²⁷ [i]