MinT - Best Known (228−155, 228, s)-Nets in Base 4

Best Known (228−155, 228, s)-Nets in Base 4

(228−155, 228, 104)-Net over F₄ — Constructive and digital

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]

(228−155, 228, 112)-Net over F₄ — Digital

Digital (73, 228, 112)-net over F₄, using

net from sequence [i] based on digital (73, 111)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
  - Drinfeld modules of rank 1 [i]

(228−155, 228, 524)-Net in Base 4 — Upper bound on s

There is no (73, 228, 525)-net in base 4, because

1 times m-reduction [i] would yield (73, 227, 525)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51786 430619 526964 839411 927316 764014 438041 983874 192836 181197 581407 198464 774144 627970 191841 808295 612100 726967 745877 937011 568062 945431 309664 > 4²²⁷ [i]